Past Probability Seminars Spring 2020: Difference between revisions

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== Fall 2013 ==
= Spring 2018 =


<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>


Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted.  
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.


<b>
<!-- == Thursday, January 25, 2018, TBA== -->
Visit [https://mailman.cae.wisc.edu/listinfo/apseminar this page] to sign up for the email list to receive seminar announcements.</b>


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


== Thursday, September 12, Tom Kurtz, UW-Madison ==
Title: '''A remark on long-range repulsion in spectrum'''


Title: <b> Particle representations for SPDEs with boundary conditions </b>
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.


Abstract: Stochastic partial differential equations frequently arise as limits of finite systems of weighted interacting particles. For a variety of purposes, it is useful to keep the particles in the limit obtaining an infinite exchangeable system of stochastic differential equations for the particle locations and weights. The corresponding de Finetti measure then gives the solution of the SPDE. These representations frequently simplify existence, uniqueness and convergence results. Following some discussion of general approaches to SPDEs, the talk will focus on situations where the particle locations are given by an iid family of diffusion processes, and the weights are chosen to obtain a nonlinear driving term and to match given boundary conditions for the SPDE. (Recent results are joint work with Dan Crisan.)
== Thursday, February 8, 2018, [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==


== Thursday, September 26, David F. Anderson, UW-Madison ==
Title: '''Quantitative CLTs for random walks in random environments'''


Title: Stochastic analysis of biochemical reaction networks with absolute concentration robustness
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:   It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart "absolute concentration robustness" on a wide class of biologically relevant, deterministically modeled mass-action systems [Shinar and Feinberg, Science, 2010]. Many biochemical networks, however, operate on a scale insufficient to justify the assumptions of the deterministic mass-action model, which raises the question of whether the long-term dynamics of the systems are being accurately captured when the deterministic model predicts stability. I will discuss recent results  that  show  that fundamentally different conclusions about the long-term behavior of such systems are reached if the systems are instead modeled with stochastic dynamics and a discrete state space. Specifically we characterize a large class of models which exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space. The results are proved with a combination of methods from stochastic processes and chemical reaction network theory.
== <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 3, Lam Si Tung Ho, UW-Madison ==


Title: Asymptotic theory of Ornstein-Uhlenbeck tree models
<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: Tree models arise in evolutionary biology when sampling biological species, which are related to each other according to a phylogenetic tree. When observations are modeled using an Ornstein-Uhlenbeck (OU) process along the tree, the autocorrelation between two tips decreases exponentially with their tree distance. Under these models, tips represent biological species and the OU process parameters represent the strength and direction of natural selection. For the mean, we show that if the heights of the trees are bounded, then it is not microergodic: no estimator can ever be consistent for this parameter. On the other hand, if the heights of the trees converge to infinity, then the MLE of the mean is consistent and we establish a phase transition on the behavior of its variance. For covariance parameters, we give a general sufficient condition ensuring microergodicity. We also provide a <math>\sqrt{n}</math>-consistent estimators for them under some mild conditions.
Title: '''The fractal nature of the Abelian Sandpile'''


== Thursday, October 10, <span style="color:red">NO SEMINAR </span>==
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.


[http://www.math.northwestern.edu/mwp/ Midwest Probability Colloquium]
== Thursday, February 15, 2018, Benedek Valkó, UW-Madison ==


== <span style="color:red">Tuesday, October 15, 4pm, Van Vleck B239,</span> [http://www.math.wisc.edu/distinguished-lectures Distinguished Lecture Series in Mathematics:] [http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin], MIT ==
Title: '''Random matrices, operators and analytic functions'''


Please note the non-standard time and day.
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.  


Title: '''Integrable Probability I'''
Joint with B. Virág (Toronto/Budapest).


Abstract: The goal of the talks is to describe the emerging field of integrable
== 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]==
probability, whose goal is to identify and analyze exactly solvable
probabilistic models. The models and results are often easy to describe,
yet difficult to find, and they carry essential information about broad
universality classes of stochastic processes.


== <span style="color:red">Wednesday October 16, 2:30pm, Van Vleck B139,</span> [http://www.math.wisc.edu/distinguished-lectures Distinguished Lecture Series in Mathematics:] [http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin], MIT ==
Title: '''Estimation of large-scale time series network models'''
 
 
Please note the non-standard time and day.
 
Title: '''Integrable Probability II'''
 
Abstract: The goal of the talks is to describe the emerging field of integrable
probability, whose goal is to identify and analyze exactly solvable
probabilistic models. The models and results are often easy to describe,
yet difficult to find, and they carry essential information about broad
universality classes of stochastic processes.
 
== <span style="color:red"> Tuesday, October 22, 4pm, Van Vleck 901</span>, Anton Wakolbinger, Goethe Universität Frankfurt ==
 
Please note the non-standard time and day, <b><span style="color:red">and the recently revised time and room</span>.</b>
 
Title: '''The time to fixation of a strongly beneficial mutant in a structured population'''
 
Abstract:
We discuss a system that describes the evolution of the vector of relative frequencies of a beneficial allele in d colonies, starting in (0,...,0) and ending in (1,...,1). Its diffusion part consists of Wright-Fisher noises in all the components that model the random reproduction, its drift part consists of a linear interaction term coming from the gene flow between the colonies, together with a logistic growth term due to the selective advantage of the allele, and a term which makes the entrance from (0,...,0) possible. It turns out that there are d extremal ones among the solutions of the system, each of them corresponding to one colony in which the beneficial mutant originally appears. We then focus on the fixation time in the limit of a large selection coefficient, and explain how its asymptotic distribution can be analysed in terms of the so called ancestral selection graph.  This is joint work with Andreas Greven, Peter Pfaffelhuber and Cornelia Pokalyuk.
 
== Thursday, October 24, Ke Wang, IMA  ==
 
Title: Random weighted projections, random quadratic forms and random eigenvectors
 
Abstract: We start with a simple, yet useful, concentration inequality concerning random
weighted projections in high dimensional spaces. The inequality is used to prove a general concentration inequality for random quadratic forms. In another application, we show the infinity norm of most unit eigenvectors of Hermitian random matrices with bounded entries is <math>O(\sqrt{\log n/n})</math>. This is joint work with Van Vu.
 
 
<!-- == Thursday, October 31, TBA ==
 
Title: TBA


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, November 7, TBA ==
== Thursday, March 8, 2018, [http://www.math.cmu.edu/~eemrah/ Elnur Emrah], [http://www.math.cmu.edu/index.php CMU] ==


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


Abstract:
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, November 14, Miklos Racz, UC Berkeley  ==
== Thursday, March 15, 2018, [http://web.mst.edu/~huwen/ Wenqing Hu] [http://math.mst.edu/ Missouri S&T]==


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


Abstract:
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, November 21, Amarjit Budhiraja, UNC-Chapel Hill ==
== Thursday, March 22, 2018, [http://math.mit.edu/~mustazee/ Mustazee Rahman], [http://math.mit.edu/index.php MIT]==


Title: TBA
Title: On shocks in the TASEP


Abstract:
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, November 28, <span style="color:red">NO SEMINAR</span> ==


[http://en.wikipedia.org/wiki/Thanksgiving Thanksgiving Holiday]
This video shows the shock forming in Burgers' equation: https://www.youtube.com/watch?v=d49agpI0vu4
-->


== Thursday, December 5, Scott Hottovy, UW-Madison ==
== Thursday, March 29, 2018, Spring Break ==
<!-- == Thursday, April 5, 2018, TBA== -->


Title: TBA
== Thursday, April 12, 2018, [http://www.math.wisc.edu/~roch/ Sebastien Roch], [http://www.math.wisc.edu/ UW-Madison]==


Abstract:
== Thursday, April 19, 2018, TBA==
 
== Thursday, April 26, 2018, TBA==
== Thursday, December 12, Nikos Zygouras, University of Warwick ==
== Thursday, May 3, 2018,TBA==
 
== Thursday, May 10, 2018, 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