Large deviations for the zero set of an analytic function with diffusing coefficients

Details Large deviations for the zero set of an analytic function with diffusing coefficients Large deviations for the zero set of an analytic function with diffusing coefficients

2005-10-11

arxiv.org/abs/math/0510237v1

Mathematics

Probability

24 pages, 5 figures

Scientific paper

The "hole probability" that the zero set of the time dependent planar Gaussian analytic function f(z,t) = sum_(n=0)^infty a_n(t) z^n/sqrt(n!), where a_n(t) are i.i.d. complex valued Ornstein-Uhlenbeck processes, does not intersect a disk of radius R for all 0

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