Random polynomials of high degree and Levy concentration of measure
By Bernard Shiffman, Steve Zelditch. 2003
50 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ee1c73fb1c18221cc661e6dd082fbf1ac6af0ece
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Citations in the corpus
- EXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDS (2013, unknown): “1 of [32].”
- Injections de Sobolev probabilistes et applications (2011, background): “On trouvera dans Shiffman-Zelditch [29] des preuves analogues pour les estimées sur les sections de fibrés holomorphes.”