Probability Seminar: Difference between revisions
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== February 2, 2023, in person: [https://mathjinsukim.com/ Jinsu Kim] (POSTECH) == | == February 2, 2023, in person: [https://mathjinsukim.com/ Jinsu Kim] (POSTECH) == | ||
'''Fast and slow mixing of continuous-time Markov chains with polynomial rates''' | |||
Continuous-time Markov chains on infinite positive integer grids with polynomial rates are often used in modeling queuing systems, molecular counts of small-size biological systems, etc. In this talk, we will discuss continuous-time Markov chains that admit either fast or slow mixing behaviors. For a positive recurrent continuous-time Markov chain, the convergence rate to its stationary distribution is typically investigated with the Lyapunov function method and canonical path method. Recently, we discovered examples that do not lend themselves easily to analysis via those two methods but are shown to have either fast mixing or slow mixing with our new technique. The main ideas of the new methodologies are presented in this talk along with their applications to stochastic biochemical reaction network theory. | |||
== February 9, 2023, in person: [https://www.math.tamu.edu/~jkuan/ Jeffrey Kuan] (Texas A&M) == | == February 9, 2023, in person: [https://www.math.tamu.edu/~jkuan/ Jeffrey Kuan] (Texas A&M) == | ||
Revision as of 23:22, 25 January 2023
Spring 2023
Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom
We usually end for questions at 3:20 PM.
ZOOM LINK. Valid only for online seminars.
If you would like to sign up for the email list to receive seminar announcements then please join our group.
January 26, 2023, in person: Evan Sorensen (UW-Madison)
The stationary horizon as a universal object for KPZ models
The last 5-10 years has seen remarkable progress in constructing the central objects of the KPZ universality class, namely the KPZ fixed point and directed landscape. In this talk, I will discuss a third central object known as the stationary horizon (SH). The SH is a coupling of Brownian motions with drifts, indexed by the real line, and it describes the unique coupled invariant measures for the directed landscape. I will talk about how the SH appears as the scaling limit of several models, including Busemann processes in last-passage percolation and the TASEP speed process. I will also discuss how the SH helps to describe the collection of infinite geodesics in all directions for the directed landscape. Based on joint work with Timo Seppäläinen and Ofer Busani.
February 2, 2023, in person: Jinsu Kim (POSTECH)
Fast and slow mixing of continuous-time Markov chains with polynomial rates
Continuous-time Markov chains on infinite positive integer grids with polynomial rates are often used in modeling queuing systems, molecular counts of small-size biological systems, etc. In this talk, we will discuss continuous-time Markov chains that admit either fast or slow mixing behaviors. For a positive recurrent continuous-time Markov chain, the convergence rate to its stationary distribution is typically investigated with the Lyapunov function method and canonical path method. Recently, we discovered examples that do not lend themselves easily to analysis via those two methods but are shown to have either fast mixing or slow mixing with our new technique. The main ideas of the new methodologies are presented in this talk along with their applications to stochastic biochemical reaction network theory.