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| = Spring 2018 = | | = Fall 2018 = |
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| <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>We usually end for questions at 3:15 PM.</b> |
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| 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 |
| | [mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu] |
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| <!-- == Thursday, January 25, 2018, TBA== -->
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| == Thursday, February 1, 2018, [https://people.math.osu.edu/nguyen.1261/ Hoi Nguyen], [https://math.osu.edu/ OSU]==
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| Title: '''A remark on long-range repulsion in spectrum'''
| | ==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest == |
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| 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.
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| == Thursday, February 8, 2018, [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==
| | Title: '''The distribution of sandpile groups of random regular graphs''' |
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| Title: '''Quantitative CLTs for random walks in random environments'''
| | 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. |
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| 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.
| | 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. |
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| == <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]==
| | <!-- ==September 13, TBA == --> |
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| | ==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] == |
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| <div style="width:400px;height:75px;border:5px solid black">
| | Title: '''Stochastic quantization of Yang-Mills''' |
| <b><span style="color:red"> This is a probability-related colloquium---Please note the unusual room, day, and time! </span></b>
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| Title: '''The fractal nature of the Abelian Sandpile'''
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| | | "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. |
| 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.
| | 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]. |
| 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.
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| == Thursday, February 15, 2018, Benedek Valkó, UW-Madison ==
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| Title: '''Random matrices, operators and analytic functions'''
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| 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.
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| Joint with B. Virág (Toronto/Budapest).
| | ==September 27, [https://www.math.wisc.edu/~seppalai/ Timo Seppäläinen] [https://www.math.wisc.edu/ UW-Madison] == |
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| == 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:'''Random walk in random environment and the Kardar-Parisi-Zhang class''' |
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| | 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). |
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| Title: '''Estimation of large-scale time series network models'''
| | ==October 4, [https://people.math.osu.edu/paquette.30/ Elliot Paquette], [https://math.osu.edu/ OSU] == |
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| Estimating networks from multi-variate time series data
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| is an important problem that arises in many applications including
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| computational neuroscience, social network analysis, and many
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| others. Prior approaches either do not scale to multiple time series
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| or rely on very restrictive parametric assumptions in order to
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| guarantee mixing. In this talk, I present two approaches that provide
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| learning guarantees for large-scale multi-variate time series. The first
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| involves a parametric GLM framework where non-linear clipping and
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| saturation effects that guarantee mixing. The second involves a
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| non-parametric sparse additive model framework where beta-mixing
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| conditions are considered. Learning guarantees are provided in both
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| cases and theoretical results are supported both by simulation results
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| and performance comparisons on various data examples.
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| <!-- == Thursday, March 1, 2018, TBA== -->
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| == Thursday, March 8, 2018, [http://www.math.cmu.edu/~eemrah/ Elnur Emrah], [http://www.math.cmu.edu/index.php CMU] ==
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| Title: '''Busemann limits for a corner growth model with deterministic inhomogeneity'''
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| Busemann limits have become a useful tool in study of geodesics in percolation models. The
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| properties of these limits are closely related to the curvature of the limit shapes in the associated
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| growth models. In this talk, we will consider a corner growth model (CGM) with independent
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| exponential weights. The rates of the exponentials are deterministic and inhomogeneous across
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| columns and rows. (An equivalent model is the TASEP with step initial condition and with
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| particlewise and holewise deterministic disorder). In particular, the model lacks stationarity.
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| Under mild assumptions on the rates, the limit shape in our CGM exists, is concave and can
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| develop flat regions only near the axes. In contrast, flat regions can only occur away from the axes
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| in the CGM with general i.i.d. weights. This feature and stationarity have been instrumental in
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| proving the existence of the Busemann limits in past work. We will discuss how to adapt and
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| extend these arguments to establish the existence and main properties of the Busemann limits
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| in both flat and strictly concave regions for our CGM. The results we will present are from an
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| ongoing joint project with Chris Janjigian and Timo Seppäläinen.
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| == Thursday, March 15, 2018, [http://web.mst.edu/~huwen/ Wenqing Hu] [http://math.mst.edu/ Missouri S&T]== | | ==October 11, [https://www.math.utah.edu/~janjigia/ Chris Janjigian], [https://www.math.utah.edu/ University of Utah] == |
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| Title: '''A random perturbation approach to some stochastic approximation algorithms in optimization'''
| | ==October 18-20, [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium], No Seminar == |
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| 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).
| | ==October 25, [http://stat.columbia.edu/department-directory/name/promit-ghosal/ Promit Ghosal], Columbia == |
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| == Thursday, March 22, 2018, [http://math.mit.edu/~mustazee/ Mustazee Rahman], [http://math.mit.edu/index.php MIT]== | | ==November 1, TBA == |
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| == Thursday, March 29, 2018, Spring Break == | | ==November 8, [https://cims.nyu.edu/~thomasl/ Thomas Leblé], NYU == |
| <!-- == Thursday, April 5, 2018, TBA== -->
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| == Thursday, April 12, 2018, [http://www.math.wisc.edu/~roch/ Sebastien Roch], [http://www.math.wisc.edu/ UW-Madison]== | | ==November 15, TBA == |
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| == Thursday, April 19, 2018, TBA== | | ==November 22, [https://en.wikipedia.org/wiki/Thanksgiving Thanksgiving] Break, No Seminar == |
| == Thursday, April 26, 2018, TBA==
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| == Thursday, May 3, 2018,TBA==
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| == Thursday, May 10, 2018, TBA==
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| | ==November 29, TBA == |
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| | ==December 6, TBA == |
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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.
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].
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).
November 1, TBA
November 15, TBA
November 22, Thanksgiving Break, No Seminar
November 29, TBA
December 6, TBA
Past Seminars