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February 2021 Band-limited mimicry of point processes by point processes supported on a lattice
Jeffrey C. Lagarias, Brad Rodgers
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Ann. Appl. Probab. 31(1): 351-376 (February 2021). DOI: 10.1214/20-AAP1592

Abstract

We say that one point process on the line R mimics another at a bandwidth B if for each n1 the two point processes have n-level correlation functions that agree when integrated against all band-limited test functions on bandwidth [B,B]. This paper asks the question of for what values a and B can a given point process on the real line be mimicked at bandwidth B by a point process supported on the lattice aZ. For Poisson point processes we give a complete answer for allowed parameter ranges (a,B), and for the sine process we give existence and nonexistence regions for parameter ranges. The results for the sine process have an application to the alternative hypothesis regarding the scaled spacing of zeros of the Riemann zeta function, given in a companion paper.

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Jeffrey C. Lagarias. Brad Rodgers. "Band-limited mimicry of point processes by point processes supported on a lattice." Ann. Appl. Probab. 31 (1) 351 - 376, February 2021. https://doi.org/10.1214/20-AAP1592

Information

Received: 1 July 2019; Revised: 1 February 2020; Published: February 2021
First available in Project Euclid: 8 March 2021

Digital Object Identifier: 10.1214/20-AAP1592

Subjects:
Primary: 44A60, 60G55
Secondary: 94A20

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 1 • February 2021
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