@article{7669945f3aec4ab0878199b26149fd0b,

title = "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.",

keywords = "Electric field, Hyperuniformity, Spectral measure, Stationary point processes",

author = "Mikhail Sodin and Aron Wennman and Oren Yakir",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2023",

month = oct,

doi = "10.1007/s10955-023-03169-5",

language = "אנגלית",

volume = "190",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "10",

}