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

Mikhail Sodin, Aron Wennman*, Oren Yakir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number166
JournalJournal of Statistical Physics
Issue number10
StatePublished - Oct 2023


  • Electric field
  • Hyperuniformity
  • Spectral measure
  • Stationary point processes


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