TY - JOUR
T1 - Fluctuations of the Increment of the Argument for the Gaussian Entire Function
AU - Buckley, Jeremiah
AU - Sodin, Mikhail
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar curves. We introduce an inner product on finite formal linear combinations of curves (with real coefficients), that we call the signed length, which describes the limiting covariance of the increment. We also establish asymptotic normality of fluctuations.
AB - The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar curves. We introduce an inner product on finite formal linear combinations of curves (with real coefficients), that we call the signed length, which describes the limiting covariance of the increment. We also establish asymptotic normality of fluctuations.
KW - Gaussian processes
KW - Point processes
KW - Zeroes of holomorphic functions
UR - http://www.scopus.com/inward/record.url?scp=85019868195&partnerID=8YFLogxK
U2 - 10.1007/s10955-017-1813-z
DO - 10.1007/s10955-017-1813-z
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AN - SCOPUS:85019868195
SN - 0022-4715
VL - 168
SP - 300
EP - 330
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
ER -