Difference between revisions of "Probability Seminar"

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(Thursday, December 7, 2017, TBA)
(Thursday, February 22, 2018, Garvesh Raskutti UW-Madison Stats and WID)
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__NOTOC__
 
__NOTOC__
  
= Fall 2017 =
+
= 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.  
Line 8: Line 8:
 
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.
  
 +
<!-- == Thursday, January 25, 2018, TBA== -->
  
== Thursday, September 14, 2017, [https://math.temple.edu/~brider/ Brian Rider] [https://math.temple.edu/ Temple University] ==
+
== Thursday, February 1, 2018, [https://people.math.osu.edu/nguyen.1261/ Hoi Nguyen], [https://math.osu.edu/ OSU]==
  
'''A universality result for the random matrix hard edge'''
+
Title: '''A remark on long-range repulsion in spectrum'''
  
The hard edge refers to the distribution of the smallest singular value for certain ensembles of random matrices, or, and what is the same, that of the minimal point of a logarithmic gas constrained to the positive half line. For any "inverse temperature" and “quadratic" potential the possible limit laws (as the dimension, or number of particles, tends to infinity) was characterized by Jose Ramirez and myself in terms of the spectrum of a (random) diffusion generator. Here we show this picture persists for more general convex polynomial potentials. Joint work with Patrick Waters.
+
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 21, 2017, TBA==-->
+
== Thursday, February 8, 2018, [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==
  
<!-- == Thursday, September 28, 2017, TBA ==
+
Title: '''Quantitative CLTs for random walks in random environments'''
== Thursday, October 5, 2017 ==
+
== Thursday, October 12, 2017 == -->
+
== Thursday, October 19, 2017  [https://sites.google.com/wisc.edu/vjog/ Varun Jog], [https://www.engr.wisc.edu/department/electrical-computer-engineering/ UW-Madison ECE] and [https://graingerinstitute.engr.wisc.edu/ Grainger Institute] ==
+
  
Title: '''Teaching and learning in uncertainty'''
+
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.
  
Abstract:
+
== <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]==
We investigate a simple model for social learning with two characters: a teacher and a student. The teacher's goal is to teach the student the state of the world <math>\Theta</math>, however, the teacher herself is not certain about <math>\Theta</math> and needs to simultaneously learn it and teach it. We examine several natural strategies the teacher may employ to make the student learn as fast as possible. Our primary technical contribution is analyzing the exact learning rates for these strategies by studying the large deviation properties of the sign of a transient random walk on <math>\mathbb Z</math>.
+
  
== Thursday, October 26, 2017, [http://www.math.toronto.edu/matetski/ Konstantin Matetski]  [https://www.math.toronto.edu/ Toronto] ==
 
  
Title: '''The KPZ fixed point'''
+
<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'''
The KPZ fixed point is the Markov process at the centre of the KPZ universality class. In the talk we describe the exact solution of the totally asymmetric simple exclusion process, which is one of the models in the KPZ universality class, and provide a description of the KPZ fixed point in the 1:2:3 scaling limit. This is a joint work with Jeremy Quastel and Daniel Remenik.
+
  
<!--== Thursday, November 2, 2017, TBA ==-->
+
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, November 9, 2017, Chen Jia, University of Texas at Dallas  ==
+
== Thursday, February 15, 2018, Benedek Valkó, UW-Madison ==
  
 +
Title: '''Random matrices, operators and analytic functions'''
  
'''Mathematical foundation of nonequilibrium fluctuation-dissipation theorems and a biological application'''
+
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.
  
The fluctuation-dissipation theorem (FDT) for equilibrium states is one of the classical results in equilibrium statistical physics. In recent years, many efforts have been devoted to generalizing the classical FDT to systems far from equilibrium. This was considered as one of the most significant progress of nonequilibrium statistical physics over the past two decades. In this talk, I will introduce our recent work on the rigorous mathematical foundation of the nonequilibrium FDTs for inhomogeneous diffusion processes and inhomogeneous continuous-time Markov chains. I will also talk about the application of the nonequilibrium FDTs to a practical biological problem called sensory adaptation.
+
Joint with B. Virág (Toronto/Budapest).
  
== Thursday, November 16, 2017, [http://louisfan.web.unc.edu/ Louis Fan], [http://www.math.wisc.edu/ UW-Madison]   ==
+
== 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: '''Stochastic and deterministic spatial models for complex systems'''
+
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== -->
  
Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge, which is fundamental in any multi-scale modeling approach for complex systems, is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.
+
== Thursday, March 8, 2018, [http://www.math.cmu.edu/~eemrah/ Elnur Emrah], [http://www.math.cmu.edu/index.php CMU] ==
  
In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE, in particular, why naively adding diffusion terms to ordinary differential equations might fail to account for spatial dynamics in population models. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of certain population dynamics.
+
Title: '''Busemann limits for a corner growth model with deterministic inhomogeneity'''
  
== <span style="color:red"> Friday,</span> November 17, 2017, <span style="color:red"> 1pm, Van Vleck B223, </span> [http://math.depaul.edu/kliechty/ Karl Leichty] [https://csh.depaul.edu/academics/mathematical-sciences/Pages/default.aspx DePaul University] ==
+
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 Sepp&auml;l&auml;inen.
  
 +
== Thursday, March 15, 2018, [http://web.mst.edu/~huwen/ Wenqing Hu] [http://math.mst.edu/ Missouri S&T]==
  
<div style="width:400px;height:50px;border:5px solid black">
+
Title: '''A random perturbation approach to some stochastic approximation algorithms in optimization'''
<b><span style="color:red"> Please note the unusual room, day, and time </span></b>
+
</div>
+
 
+
Title: '''Nonintersecting Brownian motions on the unit circle'''
+
+
Abstract:
+
+
Nonintersecting Brownian bridges on the unit circle form a determinantal point process whose kernel is expressed in terms of a system of discrete orthogonal polynomials which may be studied using Riemann--Hilbert techniques. If the Brownian motions have a drift, then the weight of the orthogonal polynomials becomes complex. I will discuss the tacnode and k-tacnode processes, which are related to the Painleve II function, as scaling limits of Nonintersecting Brownian motions on the unit circle and will discuss some of the features and difficulties of Riemann--Hilbert analysis of discrete orthogonal polynomials with varying complex weights.
+
+
This is joint work with Dong Wang and Robert Buckingham.
+
  
== Thursday, November 30, 2017, [https://sites.google.com/site/guoxx097/welcome Xiaoqin Guo], [https://www.math.wisc.edu/ UW-Madison] ==
+
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: '''Harnack inequality, homogenization and random walks in a degenerate random environment'''
+
== Thursday, March 22, 2018, [http://math.mit.edu/~mustazee/ Mustazee Rahman], [http://math.mit.edu/index.php MIT]==
  
Abstract: Stochastic homogenization studies the effective equations or laws that characterize the large scale phenomena for systems with complicated random dynamics at microscopic levels. In this talk, we explore the relation between stochastic homogenization and a probabilistic model called random motion in a random medium. In particular we focus on dynamics on the integer lattice which is non-reversible in time and defined by a non-divergence form operator which is non-elliptic. A difficulty in studying this problem is that coefficients of the operator are allowed to be zero. Using random walks in random media, we present a Harnack inequality and a quantitative result for homogenization for this random operator. Joint work with N.Berger (TU-Munich), M.Cohen (Jerusalem) and J.-D. Deuschel (TU-Berlin).
+
== Thursday, March 29, 2018, Spring Break ==
 +
<!-- == Thursday, April 5, 2018, TBA== -->
  
<!--== Thursday, December 7, 2017, TBA ==
+
== Thursday, April 12, 2018, [http://www.math.wisc.edu/~roch/ Sebastien Roch], [http://www.math.wisc.edu/ UW-Madison]==
  
== Thursday, December 14, 2017, TBA ==
+
== Thursday, April 19, 2018, TBA==
 +
== Thursday, April 26, 2018, TBA==
 +
== Thursday, May 3, 2018,TBA==
 +
== Thursday, May 10, 2018, TBA==
  
  

Revision as of 11:11, 1 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

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