Difference between revisions of "Probability Seminar"

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(September 12, 2019, Victor Kleptsyn, CNRS)
(September 12, 2019, Victor Kleptsyn, CNRS)
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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.  
 
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.
 
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.
+
Our results are related to the Anderson localization in dimension one, providing a purely dynamical viewpoint on its proof. 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 10:33, 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. 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.

October 3, 2019, Scott Smith, UW Madison

October 10, 2019, NO SEMINAR - Midwest Probability Colloquium

October 17, 2019, Scott Hottovy, USNA

October 24, 2019, Brian Rider, Temple University

October 31, 2019, Elchanan Mossel, MIT

November 7, 2019, Tomas Berggren, KTH Stockholm

November 14, 2019, Benjamin Landon, MIT

November 21, 2019, TBA

November 28, 2019, Thanksgiving (no seminar)

December 5, 2019, Vadim Gorin, UW Madison

Past Seminars