Zeros of a random analytic function approach perfect spacing under repeated differentiation
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- by Robin Pemantle and Sneha Subramanian PDF
- Trans. Amer. Math. Soc. 369 (2017), 8743-8764 Request permission
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.References
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Additional Information
- Robin Pemantle
- Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Phildelphia, Pennsylvania 19104
- MR Author ID: 252544
- Email: pemantle@math.upenn.edu
- 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
- MR Author ID: 997357
- Email: sneha.subramanian@videa.tv
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 8743-8764
- MSC (2010): Primary 30B20, 60G55; Secondary 30C15
- DOI: https://doi.org/10.1090/tran/6929
- MathSciNet review: 3710642