Random polynomials of high degree and Levy concentration of measure

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dc.creatorShiffman, B.
dc.creatorZelditch, S.
dc.date2003-03-26
dc.date.accessioned2026-07-07T06:24:33Z
dc.date.available2026-07-07T06:24:33Z
dc.descriptionWe 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.
dc.descriptionIncludes results from our posted paper math.SG/0001102. Almost sure L^p bounds and the relationship to concentration of measure added
dc.identifierhttps://arxiv.org/abs/math/0303335
dc.identifierhttp://arxiv.org/abs/math/0303335
dc.identifierAsian J. Math. 7, Special issue dedicated to Yum-Tong Siu, (2003), 627-646.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96578
dc.subjectComplex Variables
dc.subjectAlgebraic Geometry
dc.subjectProbability
dc.titleRandom polynomials of high degree and Levy concentration of measure
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