# Difference between revisions of "Probability Seminar"

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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. | 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. | ||

− | ==September 13, TBA == | + | <!-- ==September 13, TBA == --> |

==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] == | ==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] == |

## Revision as of 19:32, 10 September 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

Title: **The distribution of sandpile groups of random regular graphs**

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.

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.