The random Weierstrass zeta function I. Existence, uniqueness, fluctuations

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.

arXiv comment41 pages

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Cited by in corpus (2)

• The random Weierstrass zeta function II. Fluctuations of the electric flux through rectifiable curves
• The link between hyperuniformity, Coulomb energy, and Wasserstein distance to Lebesgue for two-dimensional point processes