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Random complex zeroes,III. Decay of the hole probability

Authors:	Email author" target="_blank">Mikhail?Sodin Email author Boris?Tsirelson

Institution:	(1) School of Mathematics, Tel Aviv University, 69978 Tel Aviv, Israel

Abstract:	The ‘hoe probability’ that a random entire function $\psi (z) = \sum\limits_{k = 0}^\infty {\zeta _k \frac{{z^k }}{{\sqrt {k!} }}} ,$ where ζ₀, ζ₁, ... are Gaussian i.i.d. random variables, has no zeroes in the disc of radiusr decays as exp(−cr ⁴) for larger. Supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities.

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