Past Probability Seminars Spring 2020: Difference between revisions

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= Spring 2016 =
= Fall 2018 =


<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
<b>We  usually end for questions at 3:15 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>






== Thursday, January 28, [http://faculty.virginia.edu/petrov/ Leonid Petrov], [http://www.math.virginia.edu/ University of Virginia] ==
==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==


Title: '''The quantum integrable particle system on the line'''


I will discuss the higher spin six vertex model - an interacting  particle
Title: '''The distribution of sandpile groups of random regular graphs'''
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 ==
Abstract:
We study the distribution of the sandpile group of random <math>d</math>-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the <math>p</math>-Sylow subgroup of the sandpile group is a given <math>p</math>-group <math>P</math>, is proportional to <math>|\operatorname{Aut}(P)|^{-1}</math>. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.


Title: '''On some concrete criteria for quantum and stochastic confinement'''
Our results extends a recent theorem of Huang saying that the adjacency matrices of random <math>d</math>-regular directed graphs are invertible with high probability to the undirected case.


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>\mathbb{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).
<!-- ==September 13, TBA == -->


== <span style="color:green">Friday, February 5</span>, [http://www.math.ku.dk/~d.cappelletti/index.html Daniele Cappelletti], [http://www.math.ku.dk/ Copenhagen University], 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>==
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==


'''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].
Title: '''Stochastic quantization of Yang-Mills'''


Title: '''Deterministic and Stochastic Reaction Networks'''
Abstract:
"Stochastic quantization” refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise.
In this talk we start by an Abelian example where we take a symmetry-preserving lattice regularization and study the continuum limit. We will then discuss non-Abelian Yang-Mills theories and introduce a symmetry-breaking smooth regularization and restore the symmetry using a notion of gauge-equivariance. With these results we can construct dynamical Wilson loop and string observables. Based on [S., arXiv:1801.04596] and [Chandra,Hairer,S., work in progress].


Abstract:  Mathematical models of biochemical reaction networks are of great interest for the analysis of experimental data and theoretical biochemistry. Moreover, such models can be applied in a broader framework than that provided by biology. The classical deterministic model of a reaction network is a system of ordinary differential equations, and the standard stochastic model is a continuous-time Markov chain. A relationship between the dynamics of the two models can be found for compact time intervals, while the asymptotic behaviours of the two models may differ greatly. I will give an overview of these problems and show some recent development.


<!--== Thursday, February 11, TBA ==-->
<!--== 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] ==
==September 27, [https://www.math.wisc.edu/~seppalai/ Timo Seppäläinen] [https://www.math.wisc.edu/ UW-Madison] ==


Title: '''The norm of structured random matrices'''
Title:'''Random walk in random environment and the Kardar-Parisi-Zhang class'''
Abstract:This talk concerns a relationship between two much-studied classes of models  of motion in a random medium, namely random walk in random environment (RWRE) and the Kardar-Parisi-Zhang (KPZ) universality class. Barraquand and Corwin (Columbia)  discovered that in 1+1 dimensional RWRE in a dynamical beta environment the correction to the quenched large deviation principle obeys KPZ behavior.  In this talk we condition the beta walk to escape at an atypical velocity and show that the resulting Doob-transformed RWRE obeys the KPZ wandering exponent 2/3.  Based on joint work with Márton Balázs (Bristol) and Firas Rassoul-Agha (Utah).


Abstract: Understanding the spectral norm of random matrices is a problem
==October 4, [https://people.math.osu.edu/paquette.30/  Elliot Paquette], [https://math.osu.edu/ OSU] ==
of basic interest in several areas of pure and applied mathematics. While
the spectral norm of classical random matrix models is well understood,
existing methods almost always fail to be sharp in the presence of
nontrivial structure. In this talk, I will discuss new bounds on the norm
of random matrices with independent entries that are sharp under mild
conditions. These bounds shed significant light on the nature of the
problem, and make it possible to easily address otherwise nontrivial
phenomena such as the phase transition of the spectral edge of random band
matrices. I will also discuss some conjectures whose resolution would
complete our understanding of the underlying probabilistic mechanisms.


== Thursday,  March 3, [http://www.math.wisc.edu/~janjigia/ Chris Janjigian], [http://www.math.wisc.edu/ UW-Madison] ==
Title: '''Distributional approximation of the characteristic polynomial of a Gaussian beta-ensemble'''


Title: '''Large deviations for certain inhomogeneous corner growth models'''
Abstract:
The characteristic polynomial of the Gaussian beta--ensemble can be represented, via its tridiagonal model, as an entry in a product of independent random two--by--two matrices.  For a point z in the complex plane, at which the transfer matrix is to be evaluated, this product of transfer matrices splits into three independent factors, each of which can be understood as a different dynamical system in the complex plane.  Conjecturally, we show that the characteristic polynomial is always represented as product of at most three terms, an exponential of a Gaussian field, the stochastic Airy function, and a diffusion similar to the stochastic sine equation.
We explain the origins of this decomposition, and we show partial progress in establishing part of it.


Abstract:
Joint work with Diane Holcomb and Gaultier Lambert.
The corner growth model is a classical model of growth in the plane and is connected to other familiar models such as directed last passage percolation and the TASEP through various geometric maps. In the case that the waiting times are i.i.d. with exponential or geometric marginals, the model is well understood: the shape function can be computed exactly, the fluctuations around the shape function are known to be given by the Tracy-Widom GUE distribution, and large deviation principles corresponding to this limit have been derived.


This talk considers the large deviation properties of a generalization of the classical model in which the rates of the exponential are drawn randomly in an appropriate way. We will discuss some exact computations of rate functions in the quenched and annealed versions of the model, along with some interesting properties of large deviations in this model. (Based on joint work with Elnur Emrah.)
==October 11, [https://www.math.utah.edu/~janjigia/ Chris Janjigian], [https://www.math.utah.edu/ University of Utah] ==


== Thursday,  March 10, [http://www.math.wisc.edu/~jyin/jun-yin.html Jun Yin], [http://www.math.wisc.edu/ UW-Madison] ==


Title: '''Delocalization and Universality of band matrices.'''
Title: '''Busemann functions and Gibbs measures in directed polymer models on Z^2'''


Abstract: in this talk we introduce our new work on band matrices, whose eigenvectors and eigenvalues are  widely believed  to have the same asymptotic behaviors as those of Wigner matrices.
Abstract: We consider the model of a nearest-neighbor random walk on the planar square lattice in a general iid space-time potential, which is also known as a directed polymer in a random environment. We prove results on existence, uniqueness (and non-uniqueness), and the law of large numbers for semi-infinite path measures. Our main tools are the Busemann functions, which are families of stochastic processes obtained through limits of ratios of partition functions.
We proved that this conjecture is true as long as the bandwidth is wide enough.


== Thursday,  March 17, [http://www.math.wisc.edu/~roch/ Sebastien Roch], [http://www.math.wisc.edu/ UW-Madison] ==
Based on joint work with Firas Rassoul-Agha


==October 18-20, [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium], No Seminar ==


Title: '''Recovering the Treelike Trend of Evolution Despite Extensive Lateral Genetic Transfer'''
==October 25, [http://stat.columbia.edu/department-directory/name/promit-ghosal/ Promit Ghosal], Columbia ==


Abstract
Reconstructing the tree of life from molecular sequences is a fundamental problem in computational
biology. Modern data sets often contain large numbers of genes. That can complicate the reconstruction because different genes often undergo different evolutionary histories. This is the case in particular in the presence of lateral genetic transfer (LGT), where a gene is inherited from a distant species rather than an immediate ancestor. Such an event produces a gene tree which is distinct from (but related to) the species phylogeny. In this talk I will sketch recent results showing that, under a natural stochastic model of LGT, the species phylogeny can be reconstructed from gene trees despite surprisingly high rates of LGT.


== Thursday, March 24, No Seminar, Spring Break ==
Title: '''Tails of the KPZ equation'''
     
Abstract: The KPZ equation is a fundamental stochastic PDE related to modeling random growth processes, Burgers turbulence, interacting particle system, random polymers etc. It is related to another important SPDE, namely, the stochastic heat equation (SHE). In this talk, we focus on the tail probabilities of the solution of the KPZ equation. For instance, we investigate the probability of the solution being smaller or larger than the expected value. Our analysis is based on an exact identity between the KPZ equation and the Airy point process (which arises at the edge of the spectrum of the random Hermitian matrices) and the Brownian Gibbs property of the KPZ line ensemble.


== Thursday,  March 31, [http://www.ssc.wisc.edu/~whs/ Bill Sandholm], [http://www.econ.wisc.edu/ Economics, UW-Madison] ==
This talk will be based on a joint work with my advisor Prof. Ivan Corwin.


== Thursday,  April 7, TBA ==
==November 1, TBA ==


== Thursday,  April 14, [https://www.math.wisc.edu/~jessica/ Jessica Lin], [https://www.math.wisc.edu/~jessica/ UW-Madison], Joint with [https://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE Geometric Analysis seminar] ==
==November 8, [https://cims.nyu.edu/~thomasl/ Thomas Leblé], NYU ==


== Thursday, April 21, [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade], [https://www.cims.nyu.edu/ Courant Institute, NYU] ==
==November 15, TBA ==


== Thursday,  April 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] ==
==November 22, [https://en.wikipedia.org/wiki/Thanksgiving Thanksgiving] Break, No Seminar ==


== Thursday,  May 5, TBA ==
==November 29, TBA ==


== ==
==December 6, TBA ==




== ==


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

Revision as of 12:52, 3 October 2018


Fall 2018

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


Friday, August 10, 10am, B239 Van Vleck András Mészáros, Central European University, Budapest

Title: The distribution of sandpile groups of random regular graphs

Abstract: We study the distribution of the sandpile group of random [math]\displaystyle{ d }[/math]-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the [math]\displaystyle{ p }[/math]-Sylow subgroup of the sandpile group is a given [math]\displaystyle{ p }[/math]-group [math]\displaystyle{ P }[/math], is proportional to [math]\displaystyle{ |\operatorname{Aut}(P)|^{-1} }[/math]. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.

Our results extends a recent theorem of Huang saying that the adjacency matrices of random [math]\displaystyle{ d }[/math]-regular directed graphs are invertible with high probability to the undirected case.


September 20, Hao Shen, UW-Madison

Title: Stochastic quantization of Yang-Mills

Abstract: "Stochastic quantization” refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise. In this talk we start by an Abelian example where we take a symmetry-preserving lattice regularization and study the continuum limit. We will then discuss non-Abelian Yang-Mills theories and introduce a symmetry-breaking smooth regularization and restore the symmetry using a notion of gauge-equivariance. With these results we can construct dynamical Wilson loop and string observables. Based on [S., arXiv:1801.04596] and [Chandra,Hairer,S., work in progress].


September 27, Timo Seppäläinen UW-Madison

Title:Random walk in random environment and the Kardar-Parisi-Zhang class

Abstract:This talk concerns a relationship between two much-studied classes of models of motion in a random medium, namely random walk in random environment (RWRE) and the Kardar-Parisi-Zhang (KPZ) universality class. Barraquand and Corwin (Columbia) discovered that in 1+1 dimensional RWRE in a dynamical beta environment the correction to the quenched large deviation principle obeys KPZ behavior. In this talk we condition the beta walk to escape at an atypical velocity and show that the resulting Doob-transformed RWRE obeys the KPZ wandering exponent 2/3. Based on joint work with Márton Balázs (Bristol) and Firas Rassoul-Agha (Utah).

October 4, Elliot Paquette, OSU

Title: Distributional approximation of the characteristic polynomial of a Gaussian beta-ensemble

Abstract: The characteristic polynomial of the Gaussian beta--ensemble can be represented, via its tridiagonal model, as an entry in a product of independent random two--by--two matrices. For a point z in the complex plane, at which the transfer matrix is to be evaluated, this product of transfer matrices splits into three independent factors, each of which can be understood as a different dynamical system in the complex plane. Conjecturally, we show that the characteristic polynomial is always represented as product of at most three terms, an exponential of a Gaussian field, the stochastic Airy function, and a diffusion similar to the stochastic sine equation. We explain the origins of this decomposition, and we show partial progress in establishing part of it.

Joint work with Diane Holcomb and Gaultier Lambert.

October 11, Chris Janjigian, University of Utah

Title: Busemann functions and Gibbs measures in directed polymer models on Z^2

Abstract: We consider the model of a nearest-neighbor random walk on the planar square lattice in a general iid space-time potential, which is also known as a directed polymer in a random environment. We prove results on existence, uniqueness (and non-uniqueness), and the law of large numbers for semi-infinite path measures. Our main tools are the Busemann functions, which are families of stochastic processes obtained through limits of ratios of partition functions.

Based on joint work with Firas Rassoul-Agha

October 18-20, Midwest Probability Colloquium, No Seminar

October 25, Promit Ghosal, Columbia

Title: Tails of the KPZ equation

Abstract: The KPZ equation is a fundamental stochastic PDE related to modeling random growth processes, Burgers turbulence, interacting particle system, random polymers etc. It is related to another important SPDE, namely, the stochastic heat equation (SHE). In this talk, we focus on the tail probabilities of the solution of the KPZ equation. For instance, we investigate the probability of the solution being smaller or larger than the expected value. Our analysis is based on an exact identity between the KPZ equation and the Airy point process (which arises at the edge of the spectrum of the random Hermitian matrices) and the Brownian Gibbs property of the KPZ line ensemble.

This talk will be based on a joint work with my advisor Prof. Ivan Corwin.

November 1, TBA

November 8, Thomas Leblé, NYU

November 15, TBA

November 22, Thanksgiving Break, No Seminar

November 29, TBA

December 6, TBA

Past Seminars