Extremal process of the zero-average Gaussian free field for d≥3

Authors

Sayan Das, Columbia University
Rajat Subhra Hazra, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Statistics and Probability Letters

Abstract

We consider the Gaussian free field on the torus whose covariance kernel is given by the zero-average Green's function. We show that for dimension d≥3, the extremal point process associated with this field converges weakly to a Poisson random measure. As an immediate corollary the maxima of the field converges after appropriate centering and scaling to the Gumbel distribution.

First Page

42

Last Page

49

DOI

10.1016/j.spl.2018.10.020

Publication Date

3-1-2019

Recommended Citation

Das, Sayan and Hazra, Rajat Subhra, "Extremal process of the zero-average Gaussian free field for d≥3" (2019). Journal Articles. 937.
https://digitalcommons.isical.ac.in/journal-articles/937