We study zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We prove that the horizontal limiting measure of the zeroes exists almost surely, and that it is non-random if and only if the spectral measure is continuous (or degenerate). In this case, the limiting measure is computed in terms of the spectral measure. We compare the behavior with Gaussian analytic functions with symmetry around the real axis. These results extend a work by Norbert Wiener.
Bibliographical noteFunding Information:
∗ Research supported by the Science Foundation of the Israel Academy of Sciences and Humanities, grant 171/07. Received June 22, 2011
Copyright 2021 Elsevier B.V., All rights reserved.