The winding number of a Gaussian random field

H. V. Navrotskyi
Theory of Stochastic Processes
Vol.29 (45), no.2, 2025, pp.119-126
The article is devoted to the study of the winding number of a Gaussian random field on the plane. It is known that the winding number of a non-degenerate random field can be presented as a difference of two point processes. The non-degeneracy is proved. It is further proved that the corresponding point processes are simple, locally finite, stationary and mixing.
DOI: https://doi.org/10.3842/tsp-4875917408-76
Full version