# Difference between revisions of "Probability Seminar"

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− | = | + | = Fall 2019 = |

− | <b>Thursdays in 901 Van Vleck Hall at 2: | + | <b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. |

− | <b>We usually end for questions at 3: | + | <b>We usually end for questions at 3:20 PM.</b> |

− | 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. | + | If you would like to sign up for the email list to receive seminar announcements then please send an email to |

+ | [mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu] | ||

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− | == | + | == 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 3, 2019, Scott Smith, UW Madison == |

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

− | + | == 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 == |

− | + | == 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 28, 2019, Thanksgiving (no seminar) == |

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

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+ | == <span style="color:red"> Wednesday, February 6 at 4:00pm in Van Vleck 911</span> , [https://lc-tsai.github.io/ Li-Cheng Tsai], [https://www.columbia.edu/ Columbia University] == | ||

+ | Title: '''When particle systems meet PDEs''' | ||

− | + | Abstract: Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.. | |

− | < | + | == <span style="color:red">'''Tuesday''' </span>, May 7, Van Vleck 901, 2:25pm, Duncan Dauvergne (Toronto) == |

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− | <div style="width: | + | <div style="width:250px;height:50px;border:5px solid black"> |

− | <b><span style="color:red"> Please note the unusual day | + | <b><span style="color:red">  Please note the unusual day. |

− | </b> | + |   </span></b> |

</div> | </div> | ||

+ | Title: '''The directed landscape''' | ||

− | + | Abstract: I will describe the construction of the full scaling limit of (Brownian) last passage percolation: the directed landscape. The directed landscape can be thought of as a random scale-invariant `directed' metric on the plane, and last passage paths converge to directed geodesics in this metric. The directed landscape is expected to be a universal scaling limit for general last passage and random growth models (i.e. TASEP, the KPZ equation, the longest increasing subsequence in a random permutation). Joint work with Janosch Ormann and Balint Virag. | |

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## Latest revision as of 17:11, 16 September 2019

# Fall 2019

**Thursdays in 901 Van Vleck Hall at 2:30 PM**, unless otherwise noted.
**We usually end for questions at 3:20 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.