Past Probability Seminars Spring 2020: Difference between revisions

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= Fall 2014 =
= Spring 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 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 join-probsem@lists.wisc.edu.


<!-- [[File:probsem.jpg]] -->
<!-- == Thursday, January 25, 2018, TBA== -->
</b>
 
= =
 
== Thursday, September 11, <span style="color:red">Van Vleck B105,</span> [http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood], UW-Madison ==
 
Please note the non-standard room.
 
Title: '''The distribution of sandpile groups of random graphs'''
 
Abstract:<br>
The sandpile group is an abelian group associated to a graph, given as
the cokernel of the graph Laplacian.  An Erdős–Rényi random graph
then gives some distribution of random abelian groups.  We will give
an introduction to various models of random finite abelian groups
arising in number theory and the connections to the distribution
conjectured by Payne et. al. for sandpile groups.  We will talk about
the moments of random finite abelian groups, and how in practice these
are often more accessible than the distributions themselves, but
frustratingly are not a priori guaranteed to determine the
distribution.  In this case however, we have found the moments of the
sandpile groups of random graphs, and proved they determine the
measure, and have proven Payne's conjecture.
 
== Thursday, September 18, [http://www.math.purdue.edu/~peterson/ Jonathon Peterson], [http://www.math.purdue.edu/ Purdue University]  ==
 
Title: '''Hydrodynamic limits for directed traps and systems of independent RWRE'''


Abstract:
== Thursday, February 1, 2018, [https://people.math.osu.edu/nguyen.1261/ Hoi Nguyen], [https://math.osu.edu/ OSU]==


We study the evolution of a system of independent random walks in a common random environment (RWRE). Previously a hydrodynamic limit was proved in the case where the environment is such that the random walks are ballistic (i.e., transient with non-zero speed <math>$v_0 \neq 0$)</math>. In this case it was shown that the asymptotic particle density is simply translated deterministically by the speed $v_0$. In this talk we will consider the more difficult case of RWRE that are transient but with $v_0=0$. Under the appropriate space-time scaling, we prove a hydrodynamic limit for the system of random walks. The statement of the hydrodynamic limit that we prove is non-standard in that the evolution of the asymptotic particle density is given by the solution of a random rather than a deterministic PDE. The randomness in the PDE comes from the fact that under the hydrodynamic scaling the effect of the environment does not ``average out'' and so the specific instance of the environment chosen actually matters.
Title: '''A remark on long-range repulsion in spectrum'''


The proof of the hydrodynamic limit for the system of RWRE will be accomplished by coupling the system of RWRE with a simpler model of a system of particles in an environment of ``directed traps.'' This talk is based on joint work with Milton Jara.
Abstract: In this talk we will address a "long-range" type repulsion among the singular values of random iid matrices, as well as among the eigenvalues of random Wigner matrices. We show evidence of repulsion under  arbitrary perturbation even in matrices of discrete entry distributions. In many cases our method yields nearly optimal bounds.


== Thursday, September 25, [http://math.colorado.edu/~seor3821/ Sean O'Rourke], [http://www.colorado.edu/math/ University of Colorado Boulder] ==
== Thursday, February 8, 2018, [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==


Title: '''Singular values and vectors under random perturbation'''
Title: '''Quantitative CLTs for random walks in random environments'''


Abstract:
Abstract:The classical central limit theorem (CLT) states that for sums of a large number of i.i.d. random variables with finite variance, the distribution of the rescaled sum is approximately Gaussian. However, the statement of the central limit theorem doesn't give any quantitative error estimates for this approximation. Under slightly stronger moment assumptions, quantitative bounds for the CLT are given by the Berry-Esseen estimates. In this talk we will consider similar questions for CLTs for random walks in random environments (RWRE). That is, for certain models of RWRE it is known that the position of the random walk has a Gaussian limiting distribution, and we obtain quantitative error estimates on the rate of convergence to the Gaussian distribution for such RWRE. This talk is based on joint works with Sungwon Ahn and Xiaoqin Guo.
Computing the singular values and singular vectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. A natural question is the following. How much does a small perturbation to the matrix change the singular values and vectors?


Classical (deterministic) theorems, such as those by Davis-Kahan, Wedin, and Weyl, give tight estimates for the worst-case scenario. In this talk, I will consider the case when the perturbation is random. In this setting, better estimates can be achieved when our matrix has low rank. This talk is based on joint work with Van Vu and Ke Wang.
== <span style="color:red"> Friday, 4pm </span> February 9, 2018, <span style="color:red">Van Vleck B239</span> [http://www.math.cmu.edu/~wes/ Wes Pegden], [http://www.math.cmu.edu/ CMU]==


== Thursday, October 2, [http://www.math.wisc.edu/~jyin/jun-yin.html Jun Yin], [http://www.math.wisc.edu/ UW-Madison]  ==


Title: '''Anisotropic local laws for random matrices'''
<div style="width:400px;height:75px;border:5px solid black">
<b><span style="color:red"> This is a probability-related colloquium---Please note the unusual room, day, and time! </span></b>
</div>


Abstract:
Title: '''The fractal nature of the Abelian Sandpile'''
In this talk, we introduce a new method of deriving  local laws of random matrices.  As applications, we will show the local laws  and some universality results on general sample covariance matrices: TXX^*T^* (where $T$ is non-square deterministic matrix),  and deformed Wigner matrix: H+A (where A is deterministic symmetric matrix). Note: here $TT^*$ and $A$ could be full rank matrices.


== Thursday, October 9, No seminar due to [http://www.math.northwestern.edu/mwp/ Midwest Probability Colloquium]  ==
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor.
 
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.
No seminar due to [http://www.math.northwestern.edu/mwp/ Midwest Probability Colloquium].
 
 
== Thursday, October 16, [http://www.math.utah.edu/~firas/ Firas Rassoul-Agha], [http://www.math.utah.edu/ University of Utah]==
 
Title: '''The growth model: Busemann functions, shape, geodesics, and other stories'''
 
Abstract:
We consider the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles define solutions to variational formulas that characterize limit shapes and yield new results for Busemann functions, geodesics and the competition interface.  This is joint work with Nicos Georgiou and Timo Seppalainen.


== Thursday, February 15, 2018, Benedek Valkó, UW-Madison ==


<!-- == Thursday, October 23, TBA  ==
Title: '''Random matrices, operators and analytic functions'''


Title: TBA
Abstract: Many of the important results of random matrix theory deal with limits of the eigenvalues of certain random matrix ensembles. In this talk I review some recent results on limits of `higher level objects' related to random matrices: the limits of random matrices viewed as operators and also limits of the corresponding characteristic functions.


Abstract:
Joint with B. Virág (Toronto/Budapest).
-->


<!-- == Thursday, October 30, TBA  ==
== Thursday, February 22, 2018, [http://pages.cs.wisc.edu/~raskutti/ Garvesh Raskutti] [https://www.stat.wisc.edu/ UW-Madison Stats] and [https://wid.wisc.edu/people/garvesh-raskutti/ WID]==


Title: TBA
Title: '''Estimation of large-scale time series network models'''


Abstract:
Abstract:
Estimating networks from multi-variate time series data
is an important problem that arises in many applications including
computational neuroscience, social network analysis, and many
others. Prior approaches either do not scale to multiple time series
or rely on very restrictive parametric assumptions in order to
guarantee mixing. In this talk, I present two approaches that provide
learning guarantees for large-scale multi-variate time series. The first
involves a parametric GLM framework where non-linear clipping and
saturation effects that guarantee mixing. The second involves a
non-parametric sparse additive model framework where beta-mixing
conditions are considered. Learning guarantees are provided in both
cases and theoretical results are supported both by simulation results
and performance comparisons on various data examples.
<!-- == Thursday, March 1, 2018, TBA== -->


-->
== Thursday, March 8, 2018, [http://www.math.cmu.edu/~eemrah/ Elnur Emrah], [http://www.math.cmu.edu/index.php CMU] ==
 
== Thursday, November 6, Vadim Gorin, [http://www-math.mit.edu/people/profile.php?pid=1415 MIT]  ==
 
Title: '''Multilevel Dyson Brownian Motion and its edge limits.'''
 
Abstract: The GUE Tracy-Widom distribution is known to govern the large-time asymptotics for a variety of
interacting particle systems on one side, and the asymptotic behavior for largest eigenvalues of
random Hermitian matrices on the other side. In my talk I will explain some reasons for this
connection between two seemingly unrelated classes of stochastic systems, and how this relation can
be extended to general beta random matrices. A multilevel extension of the Dyson Brownian Motion
will be the central object in the discussion.
 
(Based on joint papers with Misha Shkolnikov.)
 
==<span style="color:red"> Friday</span>, November 7, [http://tchumley.public.iastate.edu/ Tim Chumley], [http://www.math.iastate.edu/ Iowa State University] ==
 
<span style="color:darkgreen">Please note the unusual day.</span>
 
Title: '''Random billiards and diffusion'''
 
Abstract: We introduce a class of random dynamical systems derived from billiard maps and study a certain Markov chain derived from them. We then discuss the interplay between the billiard geometry and stochastic properties of the random system.  The main results presented investigate the affect of billiard geometry on a diffusion process obtained from an appropriate scaling limit of the Markov chain.
 
== Thursday, November 13, [http://www.math.wisc.edu/~seppalai/ Timo Seppäläinen], [http://www.math.wisc.edu/ UW-Madison]==


Title: '''Variational formulas for directed polymer and percolation models'''
Title: '''Busemann limits for a corner growth model with deterministic inhomogeneity'''


Abstract:
Abstract:
Explicit formulas for subadditive limits of polymer and percolation models in probability and statistical mechanics have been difficult to find. We describe variational formulas for these limits and their connections with other features of the models such as Busemann functions and Kardar-Parisi-Zhang (KPZ) fluctuation exponents.
Busemann limits have become a useful tool in study of geodesics in percolation models. The
properties of these limits are closely related to the curvature of the limit shapes in the associated
growth models. In this talk, we will consider a corner growth model (CGM) with independent
exponential weights. The rates of the exponentials are deterministic and inhomogeneous across
columns and rows. (An equivalent model is the TASEP with step initial condition and with
particlewise and holewise deterministic disorder). In particular, the model lacks stationarity.
Under mild assumptions on the rates, the limit shape in our CGM exists, is concave and can
develop flat regions only near the axes. In contrast, flat regions can only occur away from the axes
in the CGM with general i.i.d. weights. This feature and stationarity have been instrumental in
proving the existence of the Busemann limits in past work. We will discuss how to adapt and
extend these arguments to establish the existence and main properties of the Busemann limits
in both flat and strictly concave regions for our CGM. The results we will present are from an
ongoing joint project with Chris Janjigian and Timo Sepp&auml;l&auml;inen.


== Thursday, March 15, 2018, [http://web.mst.edu/~huwen/ Wenqing Hu] [http://math.mst.edu/ Missouri S&T]==


<!--
Title: '''A random perturbation approach to some stochastic approximation algorithms in optimization'''


== Thursday, November 20, TBA ==
Abstract: Many large-scale learning problems in modern statistics and machine learning can be reduced to solving stochastic optimization problems, i.e., the search for (local) minimum points of the expectation of an objective random function (loss function). These optimization problems are usually solved by certain stochastic approximation algorithms, which are recursive update rules with random inputs in each iteration. In this talk, we will be considering various types of such stochastic approximation algorithms, including the stochastic gradient descent, the stochastic composite gradient descent, as well as the stochastic heavy-ball method. By introducing approximating diffusion processes to the discrete recursive schemes, we will analyze the convergence of the diffusion limits to these algorithms via delicate techniques in stochastic analysis and asymptotic methods, in particular random perturbations of dynamical systems. This talk is based on a series of joint works with Chris Junchi Li (Princeton), Weijie Su (UPenn) and Haoyi Xiong (Missouri S&T).


Title: TBA
== Thursday, March 22, 2018, [http://math.mit.edu/~mustazee/ Mustazee Rahman], [http://math.mit.edu/index.php MIT]==


Abstract:
Title: On shocks in the TASEP


-->
Abstract: The TASEP particle system, moving rightward, runs into traffic jams when the initial particle density to the left of the origin is smaller than the density to the right. The density function satisfies Burgers' equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP where we identify joint fluctuations of particles at the shock by using determinantal formulae for correlation functions of TASEP and its KPZ scaling limit. The limit process is expressed in terms of GOE Tracy-Widom laws.


== Thursday, December 1,  [http://www.ma.utexas.edu/users/jneeman/index.html Joe Neeman], [http://www.ma.utexas.edu/ UT-Austin], <span style="color:red">4pm, Room B239 Van Vleck Hall</span>==
This video shows the shock forming in Burgers' equation: https://www.youtube.com/watch?v=d49agpI0vu4


<span style="color:darkgreen">Please note the unusual time.</span>
== Thursday, March 29, 2018, Spring Break ==
<!-- == Thursday, April 5, 2018, TBA== -->


Title: Some phase transitions in the stochastic block model
== Thursday, April 12, 2018, [http://www.math.wisc.edu/~roch/ Sebastien Roch], [http://www.math.wisc.edu/ UW-Madison]==


Abstract: The stochastic block model is a random graph model that was originally 30 years ago to study community detection in networks. To generate a random graph from this model, begin with two classes of vertices and then connect each pair of vertices independently at random, with probability p if they are in the same class and probability q otherwise. Some questions come to mind: can we reconstruct the classes if we only observe the graph? What if we only want to partially reconstruct the classes? How different is this model from an Erdos-Renyi graph anyway? The answers to these questions depend on p and q, and we will say exactly how.
== Thursday, April 19, 2018, TBA==
== Thursday, April 26, 2018, TBA==
== Thursday, May 3, 2018,TBA==
== Thursday, May 10, 2018, TBA==


== Thursday, December 4, Arjun Krishnan, [http://www.fields.utoronto.ca/ Fields Institute] ==


Title: TBA


Abstract:
== Thursday, December 11, TBA  ==
Title: TBA
Abstract:


== ==
== ==


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

Revision as of 16:24, 9 March 2018


Spring 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.


Thursday, February 1, 2018, Hoi Nguyen, OSU

Title: A remark on long-range repulsion in spectrum

Abstract: In this talk we will address a "long-range" type repulsion among the singular values of random iid matrices, as well as among the eigenvalues of random Wigner matrices. We show evidence of repulsion under arbitrary perturbation even in matrices of discrete entry distributions. In many cases our method yields nearly optimal bounds.

Thursday, February 8, 2018, Jon Peterson, Purdue

Title: Quantitative CLTs for random walks in random environments

Abstract:The classical central limit theorem (CLT) states that for sums of a large number of i.i.d. random variables with finite variance, the distribution of the rescaled sum is approximately Gaussian. However, the statement of the central limit theorem doesn't give any quantitative error estimates for this approximation. Under slightly stronger moment assumptions, quantitative bounds for the CLT are given by the Berry-Esseen estimates. In this talk we will consider similar questions for CLTs for random walks in random environments (RWRE). That is, for certain models of RWRE it is known that the position of the random walk has a Gaussian limiting distribution, and we obtain quantitative error estimates on the rate of convergence to the Gaussian distribution for such RWRE. This talk is based on joint works with Sungwon Ahn and Xiaoqin Guo.

Friday, 4pm February 9, 2018, Van Vleck B239 Wes Pegden, CMU

This is a probability-related colloquium---Please note the unusual room, day, and time!

Title: The fractal nature of the Abelian Sandpile

Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.

Thursday, February 15, 2018, Benedek Valkó, UW-Madison

Title: Random matrices, operators and analytic functions

Abstract: Many of the important results of random matrix theory deal with limits of the eigenvalues of certain random matrix ensembles. In this talk I review some recent results on limits of `higher level objects' related to random matrices: the limits of random matrices viewed as operators and also limits of the corresponding characteristic functions.

Joint with B. Virág (Toronto/Budapest).

Thursday, February 22, 2018, Garvesh Raskutti UW-Madison Stats and WID

Title: Estimation of large-scale time series network models

Abstract: Estimating networks from multi-variate time series data is an important problem that arises in many applications including computational neuroscience, social network analysis, and many others. Prior approaches either do not scale to multiple time series or rely on very restrictive parametric assumptions in order to guarantee mixing. In this talk, I present two approaches that provide learning guarantees for large-scale multi-variate time series. The first involves a parametric GLM framework where non-linear clipping and saturation effects that guarantee mixing. The second involves a non-parametric sparse additive model framework where beta-mixing conditions are considered. Learning guarantees are provided in both cases and theoretical results are supported both by simulation results and performance comparisons on various data examples.

Thursday, March 8, 2018, Elnur Emrah, CMU

Title: Busemann limits for a corner growth model with deterministic inhomogeneity

Abstract: Busemann limits have become a useful tool in study of geodesics in percolation models. The properties of these limits are closely related to the curvature of the limit shapes in the associated growth models. In this talk, we will consider a corner growth model (CGM) with independent exponential weights. The rates of the exponentials are deterministic and inhomogeneous across columns and rows. (An equivalent model is the TASEP with step initial condition and with particlewise and holewise deterministic disorder). In particular, the model lacks stationarity. Under mild assumptions on the rates, the limit shape in our CGM exists, is concave and can develop flat regions only near the axes. In contrast, flat regions can only occur away from the axes in the CGM with general i.i.d. weights. This feature and stationarity have been instrumental in proving the existence of the Busemann limits in past work. We will discuss how to adapt and extend these arguments to establish the existence and main properties of the Busemann limits in both flat and strictly concave regions for our CGM. The results we will present are from an ongoing joint project with Chris Janjigian and Timo Seppäläinen.

Thursday, March 15, 2018, Wenqing Hu Missouri S&T

Title: A random perturbation approach to some stochastic approximation algorithms in optimization

Abstract: Many large-scale learning problems in modern statistics and machine learning can be reduced to solving stochastic optimization problems, i.e., the search for (local) minimum points of the expectation of an objective random function (loss function). These optimization problems are usually solved by certain stochastic approximation algorithms, which are recursive update rules with random inputs in each iteration. In this talk, we will be considering various types of such stochastic approximation algorithms, including the stochastic gradient descent, the stochastic composite gradient descent, as well as the stochastic heavy-ball method. By introducing approximating diffusion processes to the discrete recursive schemes, we will analyze the convergence of the diffusion limits to these algorithms via delicate techniques in stochastic analysis and asymptotic methods, in particular random perturbations of dynamical systems. This talk is based on a series of joint works with Chris Junchi Li (Princeton), Weijie Su (UPenn) and Haoyi Xiong (Missouri S&T).

Thursday, March 22, 2018, Mustazee Rahman, MIT

Title: On shocks in the TASEP

Abstract: The TASEP particle system, moving rightward, runs into traffic jams when the initial particle density to the left of the origin is smaller than the density to the right. The density function satisfies Burgers' equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP where we identify joint fluctuations of particles at the shock by using determinantal formulae for correlation functions of TASEP and its KPZ scaling limit. The limit process is expressed in terms of GOE Tracy-Widom laws.

This video shows the shock forming in Burgers' equation: https://www.youtube.com/watch?v=d49agpI0vu4

Thursday, March 29, 2018, Spring Break

Thursday, April 12, 2018, Sebastien Roch, UW-Madison

Thursday, April 19, 2018, TBA

Thursday, April 26, 2018, TBA

Thursday, May 3, 2018,TBA

Thursday, May 10, 2018, TBA

Past Seminars