Extreme values for two-dimensional discrete Gaussian free field
Jian Ding, Ofer Zeitouni
TL;DR
This paper investigates the geometric structure and statistical properties of near-maximum values of the two-dimensional discrete Gaussian free field, providing estimates on maxima gaps and tail behaviors.
Contribution
It offers new insights into the geometry of near maxima, maximum gaps, and tail estimates for the 2D discrete Gaussian free field.
Findings
Description of the geometry of near maxima
Estimate on the gap between the two largest maxima
Right tail estimate for the centered maximum
Abstract
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and an estimate for the right tail up to a multiplicative constant on the law of the centered maximum.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Geometry and complex manifolds