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.
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Supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities.
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Sodin, M., Tsirelson, B. Random complex zeroes, III. Decay of the hole probability. Isr. J. Math. 147, 371–379 (2005). https://doi.org/10.1007/BF02785373
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DOI: https://doi.org/10.1007/BF02785373