Probability Seminar: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
No edit summary
 
(82 intermediate revisions by 7 users not shown)
Line 1: Line 1:
__NOTOC__
__NOTOC__
[[Probability | Back to Probability Group]]


= Spring 2022 =
[[Past Seminars]]


<b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b>  
= Spring 2024 =
<b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b>


We usually end for questions at 3:20 PM.
We usually end for questions at 3:20 PM.


[https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM LINK. Valid only for online seminars.]
== January 25, 2024: Tatyana Shcherbina (UW-Madison) ==
'''Characteristic polynomials of sparse non-Hermitian random matrices'''


If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].
We consider the asymptotic local behavior of the second correlation functions of the characteristic polynomials of sparse non-Hermitian random matrices $X_n$ whose entries have the form $x_{jk}=d_{jk}w_{jk}$ with iid complex standard Gaussian $w_{jk}$ and normalized iid Bernoulli$(p)$ $d_{jk}$.  If $p\to\infty$, the local asymptotic behavior of the second correlation function of characteristic polynomials near $z_0\in \mathbb{C}$ coincides with those for  Ginibre ensemble of non-Hermitian matrices with iid Gaussian entries: it converges to a determinant of the Ginibre kernel in the bulk $|z_0|<1$, and it is factorized if $|z_0|>1$. It appears, however, that for the finite $p>0$, the behavior is different and it exhibits the transition between three different regimes depending on values $p$ and $|z_0|^2$.  This is the joint work with Ie. Afanasiev.  


== February 1, 2024: [https://lopat.to/index.html Patrick Lopatto (Brown)] ==
'''Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices'''


== February 3, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [https://zhipengliu.ku.edu/ Zhipeng Liu] (University of Kansas)    ==
We consider two related questions about the extremal statistics of Wigner matrices (random symmetric matrices with independent entries). First, how much can their eigenvalues fluctuate? It is known that the eigenvalues of such matrices display repulsive interactions, which confine them near deterministic locations. We provide optimal estimates for this “rigidity” phenomenon. Second, what is the behavior of the maximum of the characteristic polynomial? This is motivated by a conjecture of Fyodorov–Hiary–Keating on the maxima of logarithmically correlated fields, and we will present the first results on this question for Wigner matrices. This talk is based on joint work with Paul Bourgade and Ofer Zeitouni.
== February 8, 2024: Benoit Dagallier (NYU), online talk: https://uwmadison.zoom.us/j/95724628357 ==
'''Stochastic dynamics and the Polchinski equation'''


'''One-point distribution of the geodesic in directed last passage percolation'''
I will discuss a general framework to obtain large scale information in statistical mechanics and field theory models. The basic, well known idea is to build a dynamics that samples from the model and control its long time behaviour. There are many ways to build such a dynamics, the Langevin dynamics being a typical example. In this talk I will introduce another, the Polchinski dynamics, based on renormalisation group ideas. The dynamics is parametrised by a parameter representing a certain notion of scale in the model under consideration. The Polchinski dynamics has a number of interesting properties that make it well suited to study large-dimensional models. It is also known under the name stochastic localisation. I will mention a number of recent applications of this dynamics, in particular to prove functional inequalities via a generalisation of Bakry and Emery's convexity-based argument. The talk is based on joint work with Roland Bauerschmidt and Thierry Bodineau and the recent review paper <nowiki>https://arxiv.org/abs/2307.07619</nowiki> .


In the recent twenty years, there has been a huge development in understanding the universal law behind a family of 2d random growth models, the so-called Kardar-Parisi-Zhang (KPZ) universality class. Especially, limiting distributions of the height functions are identified for a number of models in this class. Different from the height functions, the geodesics of these models are much less understood. There were studies on the qualitative properties of the geodesics in the KPZ universality class very recently,  but the precise limiting distributions of the geodesic locations remained unknown.
== February 15, 2024: [https://math.temple.edu/~tue86896/ Brian Rider (Temple)] ==
'''A matrix model for conditioned Stochastic Airy'''


In this talk, we will discuss our recent results on the one-point distribution of the geodesic of a representative model in the KPZ universality class, the directed last passage percolation with iid exponential weights. We will give the explicit formula of the one-point distribution of the geodesic location joint with the last passage times, and its limit when the parameters go to infinity under the KPZ scaling. The limiting distribution is believed to be universal for all the models in the KPZ universality class. We will further give some applications of our formulas.
There are three basic flavors of local limit theorems in random matrix theory, connected to the spectral bulk and the so-called soft and hard edges. There also abound a collection of more exotic limits which arise in models that posses degenerate (or “non-regular”) points in their equilibrium measure.  What is more, there is typically a natural double scaling about these non-regular points, producing limit laws that transition between the more familiar basic flavors. Here I will describe a general beta matrix model for which the appropriate double scaling limit is the Stochastic Airy Operator, conditioned on having no eigenvalues below a fixed level.  I know of no other random matrix double scaling fully characterized outside of beta = 2. This is work in progress with J. Ramirez (University of Costa Rica).


== February 10, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [https://jscalvert.github.io/ Jacob Calvert] (U.C. Berkeley)    ==
== February 22, 2024: No talk this week ==
'''TBA'''


'''Harmonic activation and transport'''
== February 29, 2024:  Zongrui Yang (Columbia) ==
'''Stationary measures for integrable models with two open boundaries'''


Models of Laplacian growth, such as diffusion-limited aggregation (DLA), describe interfaces which move in proportion to harmonic measure. I will introduce a model, called harmonic activation and transport (HAT), in which a finite subset of Z^2 is rearranged according to harmonic measure. HAT exhibits a phenomenon called collapse, whereby the diameter of the set is reduced to its logarithm over a number of steps comparable to this logarithm. I will describe how collapse can be used to prove the existence of the stationary distribution of HAT, which is supported on a class of sets viewed up to translation. Lastly, I will discuss the problem of quantifying the least positive harmonic measure as a function of set cardinality, which arises in the study of HAT, and a partial resolution of which rules out predictions about DLA from the physics literature. Based on joint work with Shirshendu Ganguly and Alan Hammond.
We present two methods to study the stationary measures of integrable systems with two open boundaries. The first method is based on Askey-Wilson signed measures, which is illustrated for the open asymmetric simple exclusion process and the six-vertex model on a strip. The second method is based on two-layer Gibbs measures and is illustrated for the geometric last-passage percolation and log-gamma polymer on a strip. This talk is based on joint works with Yizao Wang, Jacek Wesolowski, Guillaume Barraquand and Ivan Corwin.


== February 17, 2022, in person: [https://sites.math.northwestern.edu/~kivimae/ Pax Kivimae] (Northwestern University)   ==  
== March 7, 2024: Atilla Yilmaz (Temple) ==
'''Stochastic homogenization of nonconvex Hamilton-Jacobi equations'''


'''The Ground-State Energy and Concentration of Complexity in Spherical Bipartite Models'''
After giving a self-contained introduction to the qualitative homogenization of Hamilton-Jacobi (HJ) equations in stationary ergodic media in spatial dimension ''d ≥ 1'', I will focus on the case where the Hamiltonian is nonconvex, and highlight some interesting differences between: (i) periodic vs. truly random media; (ii) ''d = 1'' vs. ''d ≥ 2''; and (iii) inviscid vs. viscous HJ equations.


Bipartite spin glass models have been gaining popularity in the study of glassy systems with distinct interacting species. Recently, the annealed complexity of the pure spherical bipartite model was obtained by B. McKenna. In this talk, I will explain how to show that the low-lying complexity actually concentrates around this value, and how from this one can obtain a formula for the ground-state energy.
== March 14, 2024: Eric Foxall (UBC Okanagan) ==
'''Some uses of ordered representations in finite-population exchangeable ancestry models''' (ArXiv: https://arxiv.org/abs/2104.00193)


== February 24, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [http://math.uchicago.edu/~lbenigni/ Lucas Benigni] (University of Chicago)  ==
For a population model that encodes parent-child relations, an ordered representation is a partial or complete labelling of individuals, in order of their descendants’ long-term success in some sense, with respect to which the ancestral structure is more tractable. The two most common types are the lookdown and the spinal decomposition(s), used respectively to study exchangeable models and Markov branching processes. We study the lookdown for an exchangeable model with a fixed, arbitrary sequence of natural numbers, describing population size over time. We give a simple and intuitive construction of the lookdown via the complementary notions of forward and backward neutrality. We discuss its connection to the spinal decomposition in the setting of Galton-Watson trees. We then use the lookdown to give sufficient conditions on the population sequence for the existence of a unique infinite line of descent. For a related but slightly weaker property, takeover, the necessary and sufficient conditions are more easily expressed: infinite time passes on the coalescent time scale. The latter property is also related to the following question of identifiability: under what conditions can some or all of the lookdown labelling be determined by the unlabelled lineages? A reasonably good answer can be obtained by comparing extinction times and relative sizes of lineages.


'''Optimal delocalization for generalized Wigner matrices'''
== March 21, 2024: Semon Rezchikov (Princeton) ==
'''Renormalization, Diffusion Models, and Optimal Transport'''


We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular, we can bound their extremal coordinates with high probability. There has been an extensive amount of work on generalizing such a result, known as delocalization, to more general entry distributions. After giving a brief overview of the previous results going in this direction, we present an optimal delocalization result for matrices with sub-exponential entries for all eigenvectors. The proof is based on the dynamical method introduced by Erdos-Yau, an analysis of high moments of eigenvectors as well as new level repulsion estimates which will be presented during the talk. This is based on a joint work with P. Lopatto.
To this end, we will explain how Polchinski’s formulation of the renormalization group of a statistical field theory can be seen as a gradient flow equation for a relative entropy functional. We will review some related work applying this idea to problems in mathematical physics; subsequently, we will explain how this idea can be used to design adaptive bridge sampling schemes for lattice field theories based on diffusion models which learn the RG flow of the theory.  Based on joint work with Jordan Cotler.


== March 3, 2022, in person: [https://math.wisc.edu/staff/keating-david/ David Keating] (UW-Madison)  ==  
== March 28, 2024: Spring Break ==
'''TBA'''


'''$k$-tilings of the Aztec diamond'''
== April 4, 2024: Zijie Zhuang (Upenn)  online talk ==
'''TBA'''


We study $k$-tilings ($k$-tuples of domino tilings) of the Aztec diamond of rank $m$.  We assign a weight to each $k$-tiling, depending on the number of vertical dominos and also on the number of "interactions" between the different tilings.  We will compute the generating polynomials of the $k$-tilings by relating them to an integrable colored vertex model.  We will then prove some combinatorial results about $k$-tilings in certain limits of the interaction strength.
== April 11, 2024: Bjoern Bringman (Princeton) ==
'''TBA'''


== March 10, 2022, in person: [https://qiangwu2.github.io/martingale/ Qiang Wu] (University of Illinois Urbana-Champaign)   ==  
== April 18, 2024: Christopher Janjigian (Purdue) ==
'''TBA'''


'''Mean field spin glass models under weak external field'''
== April 25, 2024: Colin McSwiggen (NYU) ==
 
'''TBA'''
We study the fluctuation and limiting distribution of free energy in mean-field spin glass models with Ising spins under weak external fields. We prove that at high temperature, there are three regimes concerning the strength of external field $h \approx \rho N^{-\alpha}$ with $\rho,\alpha\in (0,\infty)$. In the super-critical regime $\alpha < 1/4$, the variance of the log-partition function is $\approx N^{1-4\alpha}$. In the critical regime $\alpha = 1/4$, the fluctuation is of constant order but depends on $\rho$. Whereas, in the sub-critical regime $\alpha>1/4$, the variance is $\Theta(1)$ and does not depend on $\rho$. We explicitly express the asymptotic mean and variance in all three regimes and prove Gaussian central limit theorems. Our proofs mainly follow two approaches. One utilizes quadratic coupling and Guerra's interpolation scheme for Gaussian disorder, extending to many other spin glass models. However, this approach can prove the CLT only at very high temperatures. The other one is a cluster-based approach for general symmetric disorders, first used in the seminal work of Aizenman, Lebowitz, and Ruelle (Comm. Math. Phys. 112 (1987), no. 1, 3-20) for the zero external field case. It was believed that this approach does not work if the external field is present. We show that if the external field is present but not too strong, it still works with a new cluster structure. In particular, we prove the CLT up to the critical temperature in the Sherrington-Kirkpatrick (SK) model when $\alpha \ge 1/4$. We further address the generality of this cluster-based approach. Specifically, we give similar results for the multi-species SK model and diluted SK model. Based on joint work with Partha S. Dey.
 
== March 24, 2022, in person: [http://math.columbia.edu/~sayan/ Sayan Das] (Columbia University)  ==
 
'''Path properties of the KPZ Equation and related polymers'''
 
The KPZ equation is a fundamental stochastic PDE that can be viewed as the log-partition function of continuum directed random polymer (CDRP). In this talk, we will first focus on the fractal properties of the tall peaks of the KPZ equation. This is based on separate joint works with Li-Cheng Tsai and Promit Ghosal. In the second part of the talk, we will study the KPZ equation through the lens of polymers. In particular, we will discuss localization aspects of CDRP that will shed light on certain properties of the KPZ equation such as ergodicity and limiting Bessel behaviors around the maximum. This is based on joint work with Weitao Zhu.
 
== March 31, 2022, in person: [http://willperkins.org/ Will Perkins] (University of Illinois Chicago)  ==
 
'''Potential-weighted connective constants and uniqueness of Gibbs measures'''
 
Classical gases (or Gibbs point processes) are models of gases or fluids, with particles interacting in the continuum via a density against background Poisson processes.  The major questions about these models are about phase transitions, and while these models have been studied in mathematics for over 70 years, some of the most fundamental questions remain open. After giving some background on these models, I will describe a new method for proving absence of phase transition (uniqueness of infinite volume Gibbs measures) in the low-density regime of processes interacting via a repulsive pair potential.  The method involves defining a new quantity, the "potential-weighted connective constant", and is motivated by techniques from computer science.  Joint work with Marcus Michelen.
 
== April 7, 2022, in person and on [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [https://sites.google.com/view/eliza-oreilly/home Eliza O'Reilly] (Caltech)  ==
 
'''Stochastic Geometry for Machine Learning'''
 
The Mondrian process is a stochastic process that produces a recursive partition of space with random axis-aligned cuts. It has been used in machine learning to build random forests and Laplace kernel approximations.  The construction allows for efficient online algorithms, but the restriction to axis-aligned cuts does not capture dependencies between features. By viewing the Mondrian as a special case of the stable under iterated (STIT) process in stochastic geometry, we resolve open questions about the generalization of cut directions. We utilize the theory of stationary random tessellations to show that STIT random forests achieve minimax rates for Lipschitz and $C^2$ functions and STIT random features approximate a large class of stationary kernels. This work opens many new questions at the intersection of stochastic geometry and machine learning. Based on joint work with Ngoc Mai Tran.
 
== April 14, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [https://cmps.ok.ubc.ca/about/contact/eric-foxall/ Eric Foxall] (UBC-Okanagan)  ==
 
'''Bifurcation theory of density-dependent Markov chains, well-mixed stochastic population models, and diffusively perturbed dynamical systems'''
 
Abstract: A common choice for modeling a finite, interacting population of individuals is to specify a variable system size parameter $N$, and to otherwise assume that interactions are well-mixed. When the model is cast in continuous time, has finitely many types, and is otherwise fairly simple, the vector $X$ of population sizes is a density-dependent Markov chain (DDMC), and the population density vector $\frac{X}{N}$ can be roughly seen as a diffusive perturbation of a deterministic system, with noise parameter $\varepsilon = 1/\sqrt{N}$. The law of large numbers and central limit theorem of these models has been known since the work of Thomas Kurtz in the 1970s. Here, we study bifurcations of parametrized models of this type, as a function of $\varepsilon$. We introduce the notion of limit scales to understand the shape of fluctuations in and around the bifurcation point, and give a three-step framework for finding them. The result is an enhanced bifurcation diagram that encodes this information with the help of a few well-chosen functions. We develop the theory in detail for one-dimensional models and illustrate it for simple bifurcation types including transcritical, saddle-node, pitchfork, and the Hopf bifurcation.
 
== April 21, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: Hugo Falconet (NYU)   ==  
 
'''Metric growth dynamics in Liouville quantum gravity'''
 
Abstract:  Liouville quantum gravity (LQG) is a canonical model of random geometry. Associated with the planar Gaussian free field, this geometry with conformal symmetries was introduced in the physics literature by Polyakov in the 80’s and is conjectured to describe the scaling limit of random planar maps. In this talk, I will introduce LQG as a metric measure space and discuss recent results on the associated metric growth dynamics. The primary focus will be on the dynamics of the trace of the free field on the boundary of growing LQG balls.  Based on a joint work with Julien Dubédat.
 
== April 28, 2022, in person: [https://www.ias.edu/scholars/amol-aggarwal Amol Aggarwal] (Columbia/IAS)  ==
 
'''ASEP Speed Process'''
 
We consider the asymmetric simple exclusion process, started under step initial data, with a single second class particle at the origin. We show that the trajectory of the second class particle almost surely follows a line, whose slope is a uniform random variable in [-1, 1]. The proof is based on a combination of probabilistic couplings and effective hydrodynamic bounds arising from the ASEP's solvability under specific choices of initial data. This is joint work with Ivan Corwin and Promit Ghosal.
 
== May 5, 2022, in person: [https://people.math.gatech.edu/~dharper40/ David Harper] (Georgia Tech)  ==


== May 2, 2024: Anya Katsevich (MIT) ==
'''TBA'''
'''TBA'''
[[Past Seminars]]

Latest revision as of 14:53, 18 March 2024

Back to Probability Group

Past Seminars

Spring 2024

Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom

We usually end for questions at 3:20 PM.

January 25, 2024: Tatyana Shcherbina (UW-Madison)

Characteristic polynomials of sparse non-Hermitian random matrices

We consider the asymptotic local behavior of the second correlation functions of the characteristic polynomials of sparse non-Hermitian random matrices $X_n$ whose entries have the form $x_{jk}=d_{jk}w_{jk}$ with iid complex standard Gaussian $w_{jk}$ and normalized iid Bernoulli$(p)$ $d_{jk}$.  If $p\to\infty$, the local asymptotic behavior of the second correlation function of characteristic polynomials near $z_0\in \mathbb{C}$ coincides with those for  Ginibre ensemble of non-Hermitian matrices with iid Gaussian entries: it converges to a determinant of the Ginibre kernel in the bulk $|z_0|<1$, and it is factorized if $|z_0|>1$. It appears, however, that for the finite $p>0$, the behavior is different and it exhibits the transition between three different regimes depending on values $p$ and $|z_0|^2$.  This is the joint work with Ie. Afanasiev.  

February 1, 2024: Patrick Lopatto (Brown)

Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices

We consider two related questions about the extremal statistics of Wigner matrices (random symmetric matrices with independent entries). First, how much can their eigenvalues fluctuate? It is known that the eigenvalues of such matrices display repulsive interactions, which confine them near deterministic locations. We provide optimal estimates for this “rigidity” phenomenon. Second, what is the behavior of the maximum of the characteristic polynomial? This is motivated by a conjecture of Fyodorov–Hiary–Keating on the maxima of logarithmically correlated fields, and we will present the first results on this question for Wigner matrices. This talk is based on joint work with Paul Bourgade and Ofer Zeitouni.

February 8, 2024: Benoit Dagallier (NYU), online talk: https://uwmadison.zoom.us/j/95724628357

Stochastic dynamics and the Polchinski equation

I will discuss a general framework to obtain large scale information in statistical mechanics and field theory models. The basic, well known idea is to build a dynamics that samples from the model and control its long time behaviour. There are many ways to build such a dynamics, the Langevin dynamics being a typical example. In this talk I will introduce another, the Polchinski dynamics, based on renormalisation group ideas. The dynamics is parametrised by a parameter representing a certain notion of scale in the model under consideration. The Polchinski dynamics has a number of interesting properties that make it well suited to study large-dimensional models. It is also known under the name stochastic localisation. I will mention a number of recent applications of this dynamics, in particular to prove functional inequalities via a generalisation of Bakry and Emery's convexity-based argument. The talk is based on joint work with Roland Bauerschmidt and Thierry Bodineau and the recent review paper https://arxiv.org/abs/2307.07619 .

February 15, 2024: Brian Rider (Temple)

A matrix model for conditioned Stochastic Airy

There are three basic flavors of local limit theorems in random matrix theory, connected to the spectral bulk and the so-called soft and hard edges. There also abound a collection of more exotic limits which arise in models that posses degenerate (or “non-regular”) points in their equilibrium measure.  What is more, there is typically a natural double scaling about these non-regular points, producing limit laws that transition between the more familiar basic flavors. Here I will describe a general beta matrix model for which the appropriate double scaling limit is the Stochastic Airy Operator, conditioned on having no eigenvalues below a fixed level.  I know of no other random matrix double scaling fully characterized outside of beta = 2. This is work in progress with J. Ramirez (University of Costa Rica).

February 22, 2024: No talk this week

TBA

February 29, 2024: Zongrui Yang (Columbia)

Stationary measures for integrable models with two open boundaries

We present two methods to study the stationary measures of integrable systems with two open boundaries. The first method is based on Askey-Wilson signed measures, which is illustrated for the open asymmetric simple exclusion process and the six-vertex model on a strip. The second method is based on two-layer Gibbs measures and is illustrated for the geometric last-passage percolation and log-gamma polymer on a strip. This talk is based on joint works with Yizao Wang, Jacek Wesolowski, Guillaume Barraquand and Ivan Corwin.

March 7, 2024: Atilla Yilmaz (Temple)

Stochastic homogenization of nonconvex Hamilton-Jacobi equations

After giving a self-contained introduction to the qualitative homogenization of Hamilton-Jacobi (HJ) equations in stationary ergodic media in spatial dimension d ≥ 1, I will focus on the case where the Hamiltonian is nonconvex, and highlight some interesting differences between: (i) periodic vs. truly random media; (ii) d = 1 vs. d ≥ 2; and (iii) inviscid vs. viscous HJ equations.

March 14, 2024: Eric Foxall (UBC Okanagan)

Some uses of ordered representations in finite-population exchangeable ancestry models (ArXiv: https://arxiv.org/abs/2104.00193)

For a population model that encodes parent-child relations, an ordered representation is a partial or complete labelling of individuals, in order of their descendants’ long-term success in some sense, with respect to which the ancestral structure is more tractable. The two most common types are the lookdown and the spinal decomposition(s), used respectively to study exchangeable models and Markov branching processes. We study the lookdown for an exchangeable model with a fixed, arbitrary sequence of natural numbers, describing population size over time. We give a simple and intuitive construction of the lookdown via the complementary notions of forward and backward neutrality. We discuss its connection to the spinal decomposition in the setting of Galton-Watson trees. We then use the lookdown to give sufficient conditions on the population sequence for the existence of a unique infinite line of descent. For a related but slightly weaker property, takeover, the necessary and sufficient conditions are more easily expressed: infinite time passes on the coalescent time scale. The latter property is also related to the following question of identifiability: under what conditions can some or all of the lookdown labelling be determined by the unlabelled lineages? A reasonably good answer can be obtained by comparing extinction times and relative sizes of lineages.

March 21, 2024: Semon Rezchikov (Princeton)

Renormalization, Diffusion Models, and Optimal Transport

To this end, we will explain how Polchinski’s formulation of the renormalization group of a statistical field theory can be seen as a gradient flow equation for a relative entropy functional. We will review some related work applying this idea to problems in mathematical physics; subsequently, we will explain how this idea can be used to design adaptive bridge sampling schemes for lattice field theories based on diffusion models which learn the RG flow of the theory.  Based on joint work with Jordan Cotler.

March 28, 2024: Spring Break

TBA

April 4, 2024: Zijie Zhuang (Upenn) online talk

TBA

April 11, 2024: Bjoern Bringman (Princeton)

TBA

April 18, 2024: Christopher Janjigian (Purdue)

TBA

April 25, 2024: Colin McSwiggen (NYU)

TBA

May 2, 2024: Anya Katsevich (MIT)

TBA