Random polynomials with prescribed newton polytope

摘要

It is well known that the Newton polytopc P of a polynomial f(z_1.,..., z_m) of degree p has a crucial influence on its value diHtributioii and in particular on its zero set. Even the number of simultaneous zeros in (C~*)~m := (C {0})~m of m generic polynomials f_i,...,f_m depends on their Newton polytopes [Be, Kol, Ko2]. Our purpose in this paper is to demonstrate that the Newton poly tope of a polynomial f also has a crucial influence on its mass density |f(z)|2dV and on the spatial distribution of zeros {/ = 0}.