Past Probability Seminars Spring 2020: Difference between revisions

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= Spring 2015 =
= Fall 2019 =


<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted.  
<b>We  usually end for questions at 3:20 PM.</b>


<b>
If you would like to sign up for the email list to receive seminar announcements then please send an email to  
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.
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
</b>


== 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.


== Thursday, January 28, [http://faculty.virginia.edu/petrov/ Leonid Petrov], [http://www.math.virginia.edu/ University of Virginia] ==
== September 19, 2019, [http://math.columbia.edu/~xuanw  Xuan Wu], Columbia University==


Title: '''The quantum integrable particle system on the line'''
'''A Gibbs resampling method for discrete log-gamma line ensemble.'''


I will discuss the higher spin six vertex model - an interacting  particle
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.
system on the discrete 1d line in the Kardar--Parisi--Zhang universality
class. Observables of this system admit explicit contour integral expressions
which degenerate  to many known formulas of such type for other integrable
systems on the line in the KPZ class, including stochastic six vertex model,
ASEP, various <math>q</math>-TASEPs, and associated zero range processes. The structure
of the higher spin six vertex model (leading to contour integral formulas for
observables) is based on Cauchy summation identities for certain symmetric
rational functions, which in turn can be traced back to the sl2 Yang--Baxter
equation. This framework allows to also include space and spin inhomogeneities
into the picture, which leads to new particle systems with unusual phase
transitions.


== Thursday, February 4, [http://homepages.math.uic.edu/~nenciu/Site/Contact.html Inina Nenciu], [http://www.math.uic.edu/ UIC], Joint Probability and Analysis Seminar ==
== October 10, 2019, NO SEMINAR - [https://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium] ==


Title: '''On some concrete criteria for quantum and stochastic confinement'''
== October 17, 2019, [https://www.usna.edu/Users/math/hottovy/index.php Scott Hottovy], USNA ==


Abstract: In this talk we will present several recent results on criteria ensuring the confinement of a quantum or a stochastic particle to a bounded domain in <math>R^n</math>. These criteria are given in terms of explicit growth and/or decay rates for the diffusion matrix and the drift potential close to the boundary of the domain. As an application of the general method, we will discuss several cases, including some where the background Riemannian manifold (induced by the diffusion matrix) is geodesically incomplete. These results are part of an ongoing joint project with G. Nenciu (IMAR, Bucharest, Romania).
''' Simplified dynamics for noisy systems with delays.'''


== <span style="color:green">Friday, February 5</span>, [http://www.math.ku.dk/~d.cappelletti/index.html Daniele Cappelletti] speaks in the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied Math Seminar], <span style="color:green">2:25pm in Room 901 </span>==
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.


'''Note:''' Daniele Cappelletti is speaking in the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied Math Seminar], but his research on stochastic reaction networks uses probability theory and is related to work of our own [http://www.math.wisc.edu/~anderson/ David Anderson].
== October 24, 2019, [https://math.temple.edu/~brider/ Brian Rider], Temple University ==


<!--== Thursday, February 11, TBA ==-->
'''A general beta crossover ensemble'''
<!--== Thursday, February 18, TBA ==-->


== Thursday, February 25, [http://www.princeton.edu/~rvan/ Ramon van Handel], [http://orfe.princeton.edu/ ORFE] and [http://www.pacm.princeton.edu/ PACM, Princeton] ==
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).


<!--== Thursday, March 3, TBA ==-->
== October 31, 2019, Vadim Gorin, UW Madison==


== Thursday,  March 10, [http://www.math.wisc.edu/~jyin/jun-yin.html Jun Yin], [http://www.math.wisc.edu/ UW-Madison] ==
'''Shift invariance for the six-vertex model and directed polymers.'''
<!--== Thursday,  March 17, TBA ==--->


== Thursday, March 24, No Seminar, Spring Break ==
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.


== Thursday, March 31, [http://www.ssc.wisc.edu/~whs/ Bill Sandholm], [http://www.econ.wisc.edu/ Economics, UW-Madison] ==
== November 7, 2019, [https://people.kth.se/~tobergg/ Tomas Berggren], KTH Stockholm ==
'''Domino tilings of the Aztec diamond with doubly periodic weightings​'''


== Thursday, April 7, 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.
== Thursday, April 14, TBA ==
   
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.


== Thursday, April 21, [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade], [https://www.cims.nyu.edu/ Courant Institute, NYU] ==
== November 14, 2019, [https://math.mit.edu/directory/profile.php?pid=2076 Benjamin Landon], MIT ==
'''Universality of extremal eigenvalue statistics of random matrices'''


== ThursdayApril 28, Nancy Garcia, [http://www.ime.unicamp.br/conteudo/departamento-estatistica Statistics], [http://www.ime.unicamp.br/ IMECC], [http://www.unicamp.br/unicamp/ UNICAMP, Brazil] ==
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.


== Thursday, May 5, TBA ==
== November 21, 2019, Tung Nguyen, UW Madison ==


== ==
'''Prevalence of deficiency zero reaction networks under an Erdos-Renyi framework
'''


Reaction network models, which are used to model many types of systems in biology, have grown dramatically in popularity over the past decade. This popularity has translated into a number of mathematical results that relate the topological features of the network to different qualitative behaviors of the associated dynamical system. One of the main topological features studied in the field is ''deficiency'' of a network. A reaction network which has strong connectivity in its connected components and a deficiency of zero is stable in both the deterministic and stochastic dynamical models.


This leads to the question: how prevalent are deficiency zero models among all such network models. In this talk, I will quantify the prevalence of deficiency zero networks among random reaction networks generated under an Erdos-Renyi framework. Specifically, with n being the number of species, I will uncover a threshold function r(n) such that the probability of the random network being deficiency zero converges to 1 if the edge probability p_n << r(n) and converges to 0 if p_n >> r(n).
== November 28, 2019, Thanksgiving (no seminar) ==
==December 5, 2019 ==


[[Past Seminars]]
[[Past Seminars]]

Revision as of 15:17, 20 November 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.

October 10, 2019, NO SEMINAR - Midwest Probability Colloquium

October 17, 2019, Scott Hottovy, USNA

Simplified dynamics for noisy systems with delays.

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.

October 24, 2019, Brian Rider, Temple University

A general beta crossover ensemble

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).

October 31, 2019, Vadim Gorin, UW Madison

Shift invariance for the six-vertex model and directed polymers.

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, Tomas Berggren, KTH Stockholm

Domino tilings of the Aztec diamond with doubly periodic weightings​

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, 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

Prevalence of deficiency zero reaction networks under an Erdos-Renyi framework

Reaction network models, which are used to model many types of systems in biology, have grown dramatically in popularity over the past decade. This popularity has translated into a number of mathematical results that relate the topological features of the network to different qualitative behaviors of the associated dynamical system. One of the main topological features studied in the field is deficiency of a network. A reaction network which has strong connectivity in its connected components and a deficiency of zero is stable in both the deterministic and stochastic dynamical models.

This leads to the question: how prevalent are deficiency zero models among all such network models. In this talk, I will quantify the prevalence of deficiency zero networks among random reaction networks generated under an Erdos-Renyi framework. Specifically, with n being the number of species, I will uncover a threshold function r(n) such that the probability of the random network being deficiency zero converges to 1 if the edge probability p_n << r(n) and converges to 0 if p_n >> r(n).

November 28, 2019, Thanksgiving (no seminar)

December 5, 2019

Past Seminars