The Random Weierstrass Zeta Function I: Existence, Uniqueness, Fluctuations

Mikhail Sodin; Aron Wennman; Oren Yakir

doi:https://doi.org/10.1007/s10955-023-03169-5

The Random Weierstrass Zeta Function I: Existence, Uniqueness, Fluctuations

Mikhail Sodin, Aron Wennman, Oren Yakir

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process. We characterize those stationary processes with finite second moment for which, after subtracting the mean, the random function becomes stationary. These random meromorphic functions can be viewed as random analogues of the Weierstrass zeta function from the theory of elliptic functions, or equivalently as electric fields generated by an infinite random distribution of point charges.

Original language	English
Article number	166
Journal	Journal of Statistical Physics
Volume	190
Issue number	10
DOIs	https://doi.org/10.1007/s10955-023-03169-5
State	Published - Oct 2023

Keywords

Electric field
Hyperuniformity
Spectral measure
Stationary point processes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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https://doi.org/10.1007/s10955-023-03169-5

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AB - We describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process. We characterize those stationary processes with finite second moment for which, after subtracting the mean, the random function becomes stationary. These random meromorphic functions can be viewed as random analogues of the Weierstrass zeta function from the theory of elliptic functions, or equivalently as electric fields generated by an infinite random distribution of point charges.

KW - Electric field

KW - Hyperuniformity

KW - Spectral measure

KW - Stationary point processes

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The Random Weierstrass Zeta Function I: Existence, Uniqueness, Fluctuations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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