Past Probability Seminars Spring 2020: Difference between revisions
| Line 12: | Line 12: | ||
== September 12, 2019, [https://perso.univ-rennes1.fr/victor.kleptsyn/ Victor Kleptsyn], CNRS == | == September 12, 2019, [https://perso.univ-rennes1.fr/victor.kleptsyn/ Victor Kleptsyn], CNRS == | ||
'''Furstenberg theorem: now with a parameter!''' | '''Furstenberg theorem: now with a parameter!''' | ||
The classical Furstenberg theorem describes the (almost sure) behaviour of a random product of independent matrices; their norms turn out to grow exponentially. In our joint work with A. Gorodetski, we study what happens if the random matrices depend on an additional parameter. | |||
It turns out that in this new situation, the conclusion changes. Namely, under some conditions, there almost surely exists a (random) "exceptional" set on parameters, on which the lower Lyapunov exponent vanishes. | |||
Our results are related to the Anderson localization in dimension one, providing a purely dynamical viewpoint on its proof. Also, I will also speak about some generalizations and related open questions. | |||
== September 19, 2019, [http://math.columbia.edu/~xuanw Xuan Wu], Columbia University== | == September 19, 2019, [http://math.columbia.edu/~xuanw Xuan Wu], Columbia University== | ||
Revision as of 16:32, 6 September 2019
Fall 2019
Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
September 12, 2019, Victor Kleptsyn, CNRS
Furstenberg theorem: now with a parameter!
The classical Furstenberg theorem describes the (almost sure) behaviour of a random product of independent matrices; their norms turn out to grow exponentially. In our joint work with A. Gorodetski, we study what happens if the random matrices depend on an additional parameter. It turns out that in this new situation, the conclusion changes. Namely, under some conditions, there almost surely exists a (random) "exceptional" set on parameters, on which the lower Lyapunov exponent vanishes. Our results are related to the Anderson localization in dimension one, providing a purely dynamical viewpoint on its proof. Also, I will also speak about some generalizations and related open questions.
September 19, 2019, Xuan Wu, Columbia University
A Gibbs resampling method for discrete log-gamma line ensemble.
In this talk we will construct the discrete log-gamma line ensemble, which is assocaited with inverse gamma polymer model. This log-gamma line ensemble enjoys a random walk Gibbs resampling invariance that follows from the integrable nature of the inverse gamma polymer model via geometric RSK correspondance. By exploiting such resampling invariance, we show the tightness of this log-gamma line ensemble under weak noise scaling. Furthermore, a Gibbs property, as enjoyed by KPZ line ensemble, holds for all subsequential limits.