Large Deviations for Zeros of P(φ)2 Random Polynomials

We extend the results of (Zeitouni and Zelditch in Int. Math. Res. Not. 2010(20): 3939-3992, 2010) on LDPs (large deviations principles) for the empirical measures Zs := 1/N Sigma(zeta:s(zeta)=0) delta zeta, (N:= #{zeta : s(zeta) = 0}) of zeros of Gaussian random polynomials s in one variable to P(phi)(2) random polynomials. The speed and rate function are the same as in the associated Gaussian case. It follows that the expected distribution of zeros in the P(phi)(2) ensembles tends to the same equilibrium measure as in the Gaussian case.