# Difference between revisions of "Probability Seminar"

(→December 19, 2019, TBA) |
(→September 12, 2019, Victor Kleptsyn, CNRS and University of Rennes 1) |
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− | == September 12, 2019, | + | == September 12, 2019, [https://perso.univ-rennes1.fr/victor.kleptsyn/ Victor Kleptsyn], CNRS and University of Rennes 1 == |

+ | '''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 where the lower limit for the 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, [http://math.columbia.edu/~xuanw 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 | + | == October 3, 2019, Scott Smith, UW Madison == |

− | == October | + | == October 10, 2019, NO SEMINAR - [https://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium] == |

− | == October | + | == October 17, 2019, [https://www.usna.edu/Users/math/hottovy/index.php Scott Hottovy], USNA == |

− | == | + | == October 24, 2019, [https://math.temple.edu/~brider/ Brian Rider], Temple University == |

− | == November 14, 2019, | + | == October 31, 2019, [http://math.mit.edu/~elmos/ Elchanan Mossel], MIT == |

+ | |||

+ | == November 7, 2019, [https://people.kth.se/~tobergg/ Tomas Berggren], KTH Stockholm == | ||

+ | |||

+ | == November 14, 2019, [https://math.mit.edu/directory/profile.php?pid=2076 Benjamin Landon], MIT == | ||

== November 21, 2019, TBA == | == November 21, 2019, TBA == | ||

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== November 28, 2019, Thanksgiving (no seminar) == | == November 28, 2019, Thanksgiving (no seminar) == | ||

− | == December 5, 2019, | + | == December 5, 2019, Vadim Gorin, UW Madison == |

## Latest revision as of 12:09, 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 and University of Rennes 1

**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 where the lower limit for the 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.