Turgay Bayraktar
Abstract: We study asymptotic patterns of zeros of random Laurent polynomials whose support are contained in dilates of a fixed integral polytope P as their degree grow. We assume that the coefficients are i.i.d. random variables whose distribution law has bounded density and logarithmically decaying tails. Along the way, we develop a pluripotential theory for plurisubharmonic functions which grow like the support function of P in the logarithmic coordinates. As a result, we prove a quantitative localized version of Bernstein-Kouchnirenko Theorem.
ArXiv: 1503.00630