EVENT DETAILS AND ABSTRACT

Title: Nodal set of random Hermite polynomials.
Speaker: Peng Zhou
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

A random Hermite polynomial on R^n is a linear combination of (properly normalized) Hermite polynomials in $n$ variables with degree $N$, with iid Gaussian coefficients. We are interested in the nodal set (zero locus) of such random polynomials, as $N$ goes to infinity. Kac-Rice formula combined with stationary phase approximation is used to derive the density of the nodal set in the “allowed region”, "forbidden region”, and the in-between “caustic region”. This is joint work with S.Zelditch and B.Hanin.