TY - JOUR
T1 - The Random Weierstrass Zeta Function I
T2 - Existence, Uniqueness, Fluctuations
AU - Sodin, Mikhail
AU - Wennman, Aron
AU - Yakir, Oren
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/10
Y1 - 2023/10
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85174540442&partnerID=8YFLogxK
U2 - 10.1007/s10955-023-03169-5
DO - 10.1007/s10955-023-03169-5
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AN - SCOPUS:85174540442
SN - 0022-4715
VL - 190
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 10
M1 - 166
ER -