Quantum ergodic sequences and equilibrium measures
Probability
2017-07-20 v1
Abstract
This is partly a survey article for Constructive Approximation's Special Issue on Approximation and Statistical Physics. It reviews results of B. Shiffman-S.Zelditch, R. Berman. S. Boucksom, D. Witt-Nystrom, T. Bloom, O. Zeitouni and others on Bergman kernels and the asymptotic equilibrium distribution of zeros of random polynomials and more general holomorphic sections of ample line bundles. The article also gives a new definition of `quantum ergodic section of a line bundle' for Hermitian line bundles with general smooth metrics and Bernstein-Markov measurs. It proves the asymptotic equilibrium distribution of zeros of these generalizaed QE sections. It also proves that random sequences and random orthonormal bases of sections are QE.
Cite
@article{arxiv.1707.06158,
title = {Quantum ergodic sequences and equilibrium measures},
author = {Steve Zelditch},
journal= {arXiv preprint arXiv:1707.06158},
year = {2017}
}