Overcrowding and hole probabilities for random zeros on complex manifolds

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dc.creatorShiffman, Bernard
dc.creatorZelditch, Steve
dc.creatorZrebiec, Scott
dc.date2008-05-16
dc.date2008-06-06
dc.date.accessioned2026-07-07T12:00:40Z
dc.date.available2026-07-07T12:00:40Z
dc.descriptionWe give asymptotic large deviations estimates for the volume inside a domain U of the zero set of a random polynomial of degree N, or more generally, of a holomorphic section of the N-th power of a positive line bundle on a compact Kaehler manifold. In particular, we show that for all $δ>0$, the probability that this volume differs by more than $δN$ from its average value is less than $\exp(-C_{δ,U}N^{m+1})$, for some constant $C_{δ,U}>0$. As a consequence, the "hole probability" that a random section does not vanish in U has an upper bound of the form $\exp(-C_{U}N^{m+1})$.
dc.description16 pages; stylistic changes, added corollary
dc.identifierhttps://arxiv.org/abs/0805.2598
dc.identifierhttp://arxiv.org/abs/0805.2598
dc.identifierIndiana Univ. Math. J. 57 (2008), 1977-1997
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/206862
dc.subjectComplex Variables
dc.subjectAlgebraic Geometry
dc.subjectProbability
dc.titleOvercrowding and hole probabilities for random zeros on complex manifolds
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