Difference between revisions of "Probability Seminar"

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(Thursday, February 15, 2018, Benedek Valk\'o)
(Friday, August 10, 10am, B239 Van Vleck András Mészáros, Central European University, Budapest)
 
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__NOTOC__
 
__NOTOC__
  
= Spring 2018 =
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= Fall 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>We  usually end for questions at 3:15 PM.</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.
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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  
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[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
  
<!-- == Thursday, January 25, 2018, TBA== -->
 
  
== Thursday, February 1, 2018, [https://people.math.osu.edu/nguyen.1261/ Hoi Nguyen], [https://math.osu.edu/ OSU]==
 
  
Title: '''A remark on long-range repulsion in spectrum'''
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==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==
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<div style="width:330px;height:70px;border:5px solid black">
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<b><span style="color:red"> ** Please note the unusual day, time, and room. **</span></b>
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</div>
  
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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Title: '''The distribution of sandpile groups of random regular graphs'''
 
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== Thursday, February 8, 2018, [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==
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Title: '''Quantitative CLTs for random walks in random environments'''
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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.
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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]==
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<div style="width:400px;height:75px;border:5px solid black">
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<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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</div>
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Title: '''The fractal nature of the Abelian Sandpile'''
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Abstract:
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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.
  
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.
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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.
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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==September 13, TBA ==
  
Title: Random matrices, operators and analytic functions
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==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==
  
Abstract: Many of the important results of random matrix theory deals with limits of the eigenvalues of certain random matrix ensembles. In this talk I review some recent results on limits of random matrices viewed as operators and also limits of the corresponding characteristic functions.
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==September 27, TBA ==
  
(Joint with B. Virág (Toronto/Budapest))
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==October 4, [https://people.math.osu.edu/paquette.30/  Elliot Paquette], [https://math.osu.edu/ OSU] ==
  
== 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]==
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==October 11, [https://www.math.utah.edu/~janjigia/ Chris Janjigian], [https://www.math.utah.edu/ University of Utah] ==
  
Title: TBA
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==October 18-20, [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium], No Seminar ==
  
<!-- == Thursday, March 1, 2018, TBA== -->
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==October 25, TBA ==
  
== Thursday, March 8, 2018, TBA==
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==November 1, TBA ==
== Thursday, March 15, 2018, [http://web.mst.edu/~huwen/ Wenqing Hu] [http://math.mst.edu/ Missouri S&T]==
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TBa
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==November 8, TBA ==
  
== Thursday, March 22, 2018, [http://math.mit.edu/~mustazee/ Mustazee Rahman], [http://math.mit.edu/index.php MIT]==
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==November 15, TBA ==
  
== Thursday, March 29, 2018, Spring Break ==
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==November 22, [https://en.wikipedia.org/wiki/Thanksgiving Thanksgiving] Break, No Seminar ==
== Thursday, April 5, 2018, TBA==
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== Thursday, April 12, 2018, TBA==
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== Thursday, April 19, 2018, TBA==
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== 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 ==
  
  

Latest revision as of 15:42, 31 July 2018


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

** Please note the unusual day, time, and room. **

Title: The distribution of sandpile groups of random regular graphs

Abstract: We study the distribution of the sandpile group of random d-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the p-Sylow subgroup of the sandpile group is a given p-group P, is proportional to |\operatorname{Aut}(P)|^{-1}. 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 d-regular directed graphs are invertible with high probability to the undirected case.

September 13, TBA

September 20, Hao Shen, UW-Madison

September 27, TBA

October 4, Elliot Paquette, OSU

October 11, Chris Janjigian, University of Utah

October 18-20, Midwest Probability Colloquium, No Seminar

October 25, TBA

November 1, TBA

November 8, TBA

November 15, TBA

November 22, Thanksgiving Break, No Seminar

November 29, TBA

December 6, TBA

Past Seminars