Convergence of random zeros on complex manifolds

Abstract

We show that the zeros of random sequences of Gaussian systems of polynomials of increasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular, the normalized distribution of zeros of systems of m polynomials of degree N, orthonormalized on a regular compact subset K of C^m, almost surely converge to the equilibrium measure on K as the degree N goes to infinity.

16 pages

References in corpus (4)

• Distribution of zeros of random and quantum chaotic sections of positive line bundles
• Universality and scaling of correlations between zeros on complex manifolds
• Exact statistical properties of the zeros of complex random polynomials
• Correlations between zeros and supersymmetry

Cited by in corpus (6)

• Zero distribution of random sparse polynomials
• Equidistribution for sequences of line bundles on normal Kaehler spaces
• Universality results for zeros of random holomorphic sections
• Hölder singular metrics on big line bundles and equidistribution
• Two point eigenvalue correlation for a class of non-selfadjoint operators under random perturbations
• Zero Distribution of Random Bernoulli Polynomial Mappings