# Probability Seminar

# Spring 2015

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

**
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**

## Thursday, January 15, Miklos Racz, UC-Berkeley Stats

Title: Testing for high-dimensional geometry in random graphs

Abstract: I will talk about a random geometric graph model, where connections between vertices depend on distances between latent d-dimensional labels; we are particularly interested in the high-dimensional case when d is large. Upon observing a graph, we want to tell if it was generated from this geometric model, or from an Erdos-Renyi random graph. We show that there exists a computationally efficient procedure to do this which is almost optimal (in an information-theoretic sense). The key insight is based on a new statistic which we call "signed triangles". To prove optimality we use a bound on the total variation distance between Wishart matrices and the Gaussian Orthogonal Ensemble. This is joint work with Sebastien Bubeck, Jian Ding, and Ronen Eldan.

## Thursday, January 22, No Seminar

## Thursday, January 29, Arnab Sen, University of Minnesota

Title: **Double Roots of Random Littlewood Polynomials**

Abstract: We consider random polynomials whose coefficients are independent and uniform on {-1,1}. We will show that the probability that such a polynomial of degree n has a double root is o(n^{-2}) when n+1 is not divisible by 4 and is of the order n^{-2} otherwise. We will also discuss extensions to random polynomials with more general coefficient distributions.

This is joint work with Ron Peled and Ofer Zeitouni.

## Thursday, February 5, TBA

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## Thursday, February 12, TBA

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## Thursday, February 19, Xiaoqin Guo, Purdue

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## Thursday, February 26, Dan Crisan, Imperial College London

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## Thursday, March 5, TBA

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## Thursday, March 12, TBA

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## Thursday, March 19, TBA

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## Thursday, March 26, Elnur Emrah, UW-Madison

Title: TBA

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