Difference between revisions of "Probability Seminar"

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(Wednesday, December 5 at 4pm in Van Vleck 911 Subhabrata Sen, MIT and Microsoft Research New England)
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__NOTOC__
 
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= Fall 2018 =
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= Spring 2019 =
  
 
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
 
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
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==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==
 
==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==
  
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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.
 
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.
  
<!-- ==September 13, TBA == -->
 
  
 
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==
 
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==
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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].
 
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].
  
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==September 27, [https://www.math.wisc.edu/~seppalai/  Timo Seppäläinen] [https://www.math.wisc.edu/ 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, [https://people.math.osu.edu/paquette.30/  Elliot Paquette], [https://math.osu.edu/ 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, [https://www.math.utah.edu/~janjigia/ Chris Janjigian], [https://www.math.utah.edu/ 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, [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium], No Seminar ==
 
 
==October 25, [http://stat.columbia.edu/department-directory/name/promit-ghosal/ 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, [https://math.umn.edu/directory/james-melbourne James Melbourne], [https://math.umn.edu/ University of Minnesota] ==
 
 
Title: '''Upper bounds on the density of independent vectors under certain linear mappings'''
 
 
Abstract:  Using functional analytic techniques and rearrangement, we prove anti-concentration results for the linear images of independent random variables, in the form of density upper bounds.  For continuous variables the results unify and sharpen Bobkov-Chistyakov's for independent sums of vectors and Rudelson-Vershynin's bounds on projections of independent coordinates.  For integer valued variables the techniques reduce finding the maximum of the probability mass function of a sum of independent variables, to the case that each variable is uniform on a contiguous interval.  This problem is approached through analysis of characteristic functions and new $L^p$ bounds on the Dirichlet and Fejer Kernel are obtained and used to derive a discrete analog of Bobkov-Chistyakov.
 
 
==November 8, [https://cims.nyu.edu/~thomasl/ Thomas Leblé], [https://cims.nyu.edu/ NYU] ==
 
 
Title: '''The Sine-beta process: DLR equations and applications'''
 
 
Abstract:
 
One-dimensional log-gases, or Beta-ensembles, are statistical physics models finding an incarnation in random matrix theory. Their limit behavior at microscopic scale is known as the Sine-beta process, its original description involves systems of coupled SDE's. In a joint work with D. Dereudre, A. Hardy, and M. Maïda, we give a new description of Sine-beta as an "infinite volume Gibbs measure", using the Dobrushin-Lanford-Ruelle (DLR) formalism, and we use it to prove the rigidity of the process, in the sense of Ghosh-Peres. Another application is a CLT for fluctuations of linear statistics.
 
 
<!-- ==November 15, TBA == -->
 
 
==November 22, [https://en.wikipedia.org/wiki/Thanksgiving Thanksgiving] Break, No Seminar ==
 
 
==  <span style="color:red">  Monday, November 26, 4pm, Van Vleck 911</span>  [http://math.mit.edu/directory/profile.php?pid=1415 Vadim Gorin], [http://math.mit.edu/index.php MIT]  ==
 
 
 
<div style="width:320px;height:50px;border:5px solid black">
 
<b><span style="color:red">&emsp; Please note the unusual day, time, <br>
 
&emsp; and room.</span></b>
 
</div>
 
 
Title: '''Macroscopic fluctuations through Schur generating functions'''
 
 
Abstract:
 
I will talk about a special class of large-dimensional stochastic systems with
 
strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices,
 
and measures governing decompositions of group representations into irreducible components.
 
 
It is believed that macroscopic fluctuations in such systems are universally
 
described by log-correlated Gaussian fields. I will present an approach to
 
handle this question based on the notion of the Schur generating function of a probability
 
distribution, and explain how it leads to a rigorous confirmation of this belief in
 
a variety of situations.
 
 
<!-- ==November 29, TBA == -->
 
 
== <span style="color:red">  Wednesday, December 5 at 4pm in Van Vleck 911</span> [http://www.mit.edu/~ssen90/ Subhabrata Sen], [https://math.mit.edu/ MIT] and [https://www.microsoft.com/en-us/research/lab/microsoft-research-new-england/ Microsoft Research New England] ==
 
 
 
<div style="width:320px;height:50px;border:5px solid black">
 
<b><span style="color:red">&emsp; Please note the unusual day, time, <br>&emsp; and room. </span></b>
 
</div>
 
 
 
 
Title: '''Random graphs, Optimization, and Spin glasses'''
 
 
Abstract:
 
Combinatorial optimization problems are ubiquitous in diverse mathematical
 
applications. The desire to understand their “typical” behavior motivates
 
a study of these problems on random instances. In spite of a long and rich
 
history, many natural questions in this domain are still intractable to rigorous
 
mathematical analysis. Graph cut problems such as Max-Cut and Min-bisection
 
are canonical examples in this class. On the other hand, physicists study these
 
questions using the non-rigorous “replica” and “cavity” methods, and predict
 
complex, intriguing features. In this talk, I will describe some recent progress
 
in our understanding of their typical properties on random graphs, obtained via
 
connections to the theory of mean-field spin glasses. The new techniques are
 
broadly applicable, and lead to novel algorithmic and statistical consequences.
 
 
 
<!-- ==December 6, TBA ==-->
 
  
 
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== ==
  
 
[[Past Seminars]]
 
[[Past Seminars]]

Revision as of 12:42, 9 January 2019


Spring 2019

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

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Past Seminars