Random polynomials of high degree and Levy concentration of measure
Abstract
Description
We show that the L^p norms of random sequences {s_N} of L^2 normalized holomorphic sections of increasing powers of an ample line bundle on a compact Kahler manifold are almost surely bounded for 2<p< infinity, and are almost surely O((log N)^{1/2}) for p= infinity. This estimate also holds for almost-holomorphic sections of positive line bundles on symplectic manifolds (in the sense of math.SG/0212180) and we give almost sure bounds for the C^k norms. Our methods involve asymptotics of Bergman-Szego kernels and the concentration of measure phenomenon.
Includes results from our posted paper math.SG/0001102. Almost sure L^p bounds and the relationship to concentration of measure added
Includes results from our posted paper math.SG/0001102. Almost sure L^p bounds and the relationship to concentration of measure added