# Probability Seminar

# Fall 2015

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

**
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**

## Thursday, September 17, Nicholas A. Cook, UCLA, 2:25pm Van Vleck B325

** Please note the unusual location, Van Vleck Hall B325 **

Title: **Random regular digraphs: singularity and spectrum**

We consider two random matrix ensembles associated to large random regular digraphs: (1) the 0/1 adjacency matrix, and (2) the adjacency matrix with iid bounded edge weights. Motivated by universality conjectures, we show that the spectral distribution for the latter ensemble is asymptotically described by the circular law, assuming the graph has degree linear in the number of vertices. Towards establishing the same result for the adjacency matrix without iid weights, we prove that it is invertible with high probability. Along the way we make use of Stein's method of exchangeable pairs to establish some graph discrepancy properties.

## Thursday, September 24, No seminar

## Thursday, October 1 Sebastien Roch, UW-Madison

## Thursday, October 8, No Seminar due to the Midwest Probability Colloquium

Midwest Probability Colloquium

## Thursday, October 15, Louis Fan, UW-Madison

## Thursday, October 22, Tom Kurtz, UW-Madison

## Thursday, October 29, Ecaterina Sava-Huss, Cornell

TBA