# 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

Title: **Mathematics of the Tree of Life--From Genomes to Phylogenetic Trees and Beyond**

Abstract: The reconstruction of the Tree of Life is an old problem in evolutionary biology which has benefited from various branches of mathematics, including probability, combinatorics, algebra, and geometry. Modern DNA sequencing technologies are producing a deluge of new data on a vast array of organisms--transforming how we view the Tree of Life and how it is reconstructed. I will survey recent progress on some mathematical and computational questions that arise in this context. No biology background will be assumed. (This is a practice run for a plenary talk at an AMS meeting.)

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

Midwest Probability Colloquium

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

Title: **Reflected diffusions with partial annihilations on a membrane (Part two)**

Abstract: Mathematicians and scientists use interacting particle models to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. In this talk, I will introduce an interacting particle system used to model the transport of positive and negative charges in solar cells. To connect the microscopic mechanisms with the macroscopic behaviors at two different scales, we show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation. This is the second part of a previous talk given in the Applied and Computation math seminar. Our proofs are based on a correlation function technique (studying the BBGKY hierarchy) and its generalization. This is joint work with Zhen-Qing Chen.

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

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

TBA