Zeros of a random analytic function approach perfect spacing under repeated differentiation

Robin Pemantle; Sneha Subramanian

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arXiv · 1409.7956

Zeros of a random analytic function approach perfect spacing under repeated differentiation

Robin Pemantle·Sneha Subramanian

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Abstract

We consider an analytic function $f$ whose zero set forms a unit intensity Poisson process on the real line. We show that repeated differentiation causes the zero set to converge in distribution to a random translate of the integers.

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Robin Pemantle, Sneha Subramanian. 2014-09-28. Zeros of a random analytic function approach perfect spacing under repeated differentiation. https://arxiv.org/abs/1409.7956

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