Zero distribution of random sparse polynomials

Abstract

We study asymptotic zero distribution of random Laurent polynomials whose support are contained in dilates of a fixed integral polytope $P$ as their degree grow. We consider a large class of probability distributions including the ones induced from i.i.d. random coefficients whose distribution law has bounded density with logarithmically decaying tails as well as moderate measures defined over the projectivized space of Laurent polynomials. We obtain a quantitative localized version of Bernstein-Kouchnirenko Theorem.

arXiv commentMinor revisions, to appear in Michigan Math. J

References in corpus (7)

• Distribution of zeros of random and quantum chaotic sections of positive line bundles
• Enumerative tropical algebraic geometry in R2
• The zeros of random polynomials cluster uniformly near the unit circle
• High Probability Analysis of the Condition Number of Sparse Polynomial Systems
• Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n
• Convergence of random zeros on complex manifolds
• Equilibrium distribution of zeros of random polynomials

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