Large deviations and random polynomials
Large deviations and random polynomials

Subhro Ghosh, Princeton University
Fine Hall 601
We consider large deviation principles (LDP) in the context of random polynomials. In one direction, we obtain a large deviations principle for the empirical measure of zeroes of random polynomials with i.i.d. exponential coefficients. One of the key challenges here is the fact that the coefficients are a.s. all positive, which enforces a growing number of highly nonlinear constraints on the locations of the zeroes. In another direction, we use LDP techniques to establish the existence of a surprising "forbidden region" in the intensity measure of zeroes of Gaussian random polynomials, when we condition on a "hole" of large radius.