##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability Seminar

## Steve Zelditch

#### Northwestern University

## Large N limit of heat kernel measure on positive Hermitian matrices and random metrics

##### Abstract:

Heat kernel measure $K(t, I, A) dA$ on positive Hermitian $NxN$ matrices is a probability measure whose large $N$ limit is important for several different types of problems in mathematical physics. My talk introduces a new application: to random Kahler metrics on any Kahler manifold. The pair correlation function of random metrics is explicitly calculated for each $N$. The large $N$ asymptotics are closely related to zero sets of random holomorphic functions.

Host: Todd Kemp

### March 10, 2016

### 9:00 AM

### AP&M 6402

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