Difference between revisions of "Probability Seminar"

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(November 14, 2019, Benjamin Landon, MIT)
(March 26, 2020, TBA)
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= Fall 2019 =
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= Spring 2020 =
  
 
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted.  
 
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted.  
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== September 12, 2019, [https://perso.univ-rennes1.fr/victor.kleptsyn/ Victor Kleptsyn], CNRS and University of Rennes 1 ==
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== January 23, 2020, Timo Seppalainen (UW Madison) ==
'''Furstenberg theorem: now with a parameter!'''
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'''Non-existence of bi-infinite geodesics in the exponential corner growth model
 +
'''
  
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.
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Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s.  A non-existence proof  in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in  November 2018. Their proof utilizes estimates from integrable probability.   This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).
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==
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== January 30, 2020, Scott Smith (UW Madison) ==
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'''TBA'''
  
'''A Gibbs resampling method for discrete log-gamma line ensemble.'''
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== February 6, 2020, Cheuk-Yin Lee (Michigan State) ==
 +
'''TBA'''
  
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.
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== February 13, 2020, Jelena Diakonikolas (UW Madison) ==
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'''TBA'''
  
== October 10, 2019, NO SEMINAR - [https://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium] ==
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== February 20, 2020, Philip Matchett Wood (UC Berkeley) ==
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'''TBA'''
  
== October 17, 2019, [https://www.usna.edu/Users/math/hottovy/index.php Scott Hottovy], USNA ==
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== February 27, 2020, TBA ==
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'''TBA'''
  
''' Simplified dynamics for noisy systems with delays.'''
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== March 5, 2020, Jiaoyang Huang (IAS) ==
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'''TBA'''
  
Many biological and physical systems include some type of random noise with a temporal delay. For example, many sperm cells travel in a random motion where their velocity changes according to a chemical signal. This chemotaxis is transmitted through a delay in the system. That is, the sperm notices chemical gradients after a certain time has elapsed.  In this case, the delay causes the sperm to aggregate around the egg. In this talk I will consider a general stochastic differential delay equation (SDDE) with state-dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero. The analysis leads to a much simpler Stochastic Differential Equation to study. The work is motivated by an experiment involving an electrical circuit with noisy, delayed feedback. The main methods used in the proof are a theorem about convergence of solutions of stochastic differential equations by Kurtz and Protter and a maximal inequality for sums of a stationary sequence of random variables by Peligrad and Utev.
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== March 12, 2020, TBA ==
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'''TBA'''
  
== October 24, 2019, [https://math.temple.edu/~brider/ Brian Rider], Temple University ==
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== March 26, 2020, Philippe Sosoe (Cornell) ==
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'''TBA'''
  
'''A general beta crossover ensemble'''
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== April 2, 2020, TBA ==
 +
'''TBA'''
  
I'll describe an operator limit for a family of general beta ensembles which exhibit a double-scaling. In particular, a free parameter in the system provides for a crossover between the more well-known  "soft" and "hard"  edge point processes.  This new limit operator takes as input the Riccati diffusion associated with the Stochastic Airy Operator. I like to suggest that this hints at a hierarchy of random operators analogous to the Painlevé hierarchy observed at the level of correlation functions for double-scaling ensembles most widely studied at beta = 2. Full disclosure: the result remains partially conjectural due to an unresolved  uniqueness question, but I’ll provide lots of evidence to convince you we have the right answer. Joint work with Jose Ramírez (Univ. Costa Rica).
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== April 9, 2020, TBA ==
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'''TBA'''
  
== October 31, 2019, Vadim Gorin, UW Madison==
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== April 16, 2020, TBA ==
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'''TBA'''
  
'''Shift invariance for the six-vertex model and directed polymers.'''
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== April 22-24, 2020, FRG Integrable Probability meeting ==
  
I will explain a recently discovered mysterious property in a variety of stochastic systems ranging  from the six-vertex model and to the directed polymers, last passage percolation, Kardar-Parisi-Zhang equation, and Airy sheet. Vaguely speaking, the property says that the multi-point joint distributions are unchanged when some (but not necessarily all!) points of observations are shifted. The property leads to explicit computations for the previously inaccessible joint distributions in all these settings.
 
  
== November 7, 2019, [https://people.kth.se/~tobergg/ Tomas Berggren], KTH Stockholm ==
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== April 30, 2020, Will Perkins (University of Illinois at Chicago) ==
'''Domino tilings of the Aztec diamond with doubly periodic weightings​'''
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'''TBA'''
  
This talk will be centered around domino tilings of the Aztec diamond with doubly periodic weightings. In particular asymptotic results of the $ 2 \times k $-periodic Aztec diamond will be discussed, both in the macroscopic and microscopic scale. The macroscopic picture is described using a close connection to a Riemann surface. For instance, the number of smooth regions (also called gas regions) is the same as the genus of the mentioned Riemann surface.
 
 
The starting point of the asymptotic analysis is a non-intersecting path formulation and a double integral formula for the correlation kernel. The proof of this double integral formula is based on joint work with M. Duits, which will be discuss briefly if time permits.
 
  
== November 14, 2019, [https://math.mit.edu/directory/profile.php?pid=2076 Benjamin Landon], MIT ==
 
```Universality of extremal eigenvalue statistics of random matrices'''
 
  
The past decade has seen significant progress on the understanding of universality of various eigenvalue statistics of random matrix theory.  However, the behavior of certain ``extremal'' or ``critical'' observables is not fully understood.  Towards the former, we discuss progress  on the universality of the largest gap between consecutive eigenvalues.  With regards to the latter, we discuss the central limit theorem for the eigenvalue counting function, which can be viewed as a linear spectral statistic with critical regularity and has logarithmically growing variance.
 
  
== November 21, 2019, Tung Nguyen, UW Madison ==
 
  
== November 28, 2019, Thanksgiving (no seminar) ==
 
  
  
==December 5, 2019 ==
 
  
 
[[Past Seminars]]
 
[[Past Seminars]]

Revision as of 12:13, 17 January 2020


Spring 2020

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


January 23, 2020, Timo Seppalainen (UW Madison)

Non-existence of bi-infinite geodesics in the exponential corner growth model

Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).

January 30, 2020, Scott Smith (UW Madison)

TBA

February 6, 2020, Cheuk-Yin Lee (Michigan State)

TBA

February 13, 2020, Jelena Diakonikolas (UW Madison)

TBA

February 20, 2020, Philip Matchett Wood (UC Berkeley)

TBA

February 27, 2020, TBA

TBA

March 5, 2020, Jiaoyang Huang (IAS)

TBA

March 12, 2020, TBA

TBA

March 26, 2020, Philippe Sosoe (Cornell)

TBA

April 2, 2020, TBA

TBA

April 9, 2020, TBA

TBA

April 16, 2020, TBA

TBA

April 22-24, 2020, FRG Integrable Probability meeting

April 30, 2020, Will Perkins (University of Illinois at Chicago)

TBA





Past Seminars