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- W1999459783 abstract "We 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 $delta>0$, the that this volume differs by more than $delta N$ from its average value is less than $exp(-C_{delta,U}N^{m+1})$, for some constant $C_{delta,U}>0$. As a consequence, the hole probability that a random section does not vanish in U has an upper bound of the form $exp(-C_{U}N^{m+1})$." @default.
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- W1999459783 date "2008-05-16" @default.
- W1999459783 modified "2023-09-23" @default.
- W1999459783 title "Overcrowding and hole probabilities for random zeros on complex manifolds" @default.
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