Convergence of the centered maximum of log-correlated gaussian fields
Document Type
Article
Publication Title
The Annals of Probability
Abstract
We show that the centered maximum of a sequence of logarithmically correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a randomly shifted Gumbel distribution, and characterize the random shift as the limit in distribution of a sequence of random variables, reminiscent of the derivative martingale in the theory of branching random walk and Gaussian chaos. We also discuss applications of the main convergence theorem and discuss examples that show that for logarithmically correlated fields; some additional structural assumptions of the type we make are needed for convergence of the centered maximum.
DOI Link
Publication Date
27-11-2017
Publisher
Project Euclid
Volume
Vol.45
Issue
Iss.6A
Recommended Citation
Ding, Jian; Roy, Rishideep; and Zeitouni, Ofer, "Convergence of the centered maximum of log-correlated gaussian fields" (2017). Faculty Publications. 508.
https://research.iimb.ac.in/fac_pubs/508
