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Transactions of the American Mathematical Society

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

Authors: Robin Pemantle and Sneha Subramanian
Journal: Trans. Amer. Math. Soc. 369 (2017), 8743-8764
MSC (2010): Primary 30B20, 60G55; Secondary 30C15
Published electronically: June 27, 2017
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Abstract: We consider an analytic function 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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Additional Information

Robin Pemantle
Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Phildelphia, Pennsylvania 19104

Sneha Subramanian
Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332-0160
Address at time of publication: Data Scientist, Videa, 3390 Peachtree Road NE, Suite 400, Atlanta, Georgia 30326

Keywords: Poisson, coefficient, saddle point, lattice, Cauchy integral, random series, translation-invariant
Received by editor(s): October 5, 2014
Received by editor(s) in revised form: March 1, 2016
Published electronically: June 27, 2017
Additional Notes: The first author’s research was supported by NSF grant DMS-1209117
Article copyright: © Copyright 2017 American Mathematical Society

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