摘要
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 set K ? ? m , almost surely converge to the equilibrium measure on K as N → ∞.
We show that the zeros of random sequences of Gaussian systems of polynomials of in- creasing 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,orthonor- malized on a regular compact set K(?)C^m,almost surely converge to the equilibrium measure on K as N→∞.
基金
Research partially supported by the Notional Science Foundation(Grant No.DMS-0600982)
