  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.
