Local picture and level-set percolation of the Gaussian free field on a large discrete torus

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Abaecherli, Angelo¹ 

[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

关键词: Gaussian free field;    Local picture;    Level-set percolation;    Discrete torus;   

DOI  :  10.1016/j.spa.2018.09.017

来源: Elsevier

【 摘 要 】

In this article we obtain for d >= 3 an approximation of the zero-average Gaussian free field on the discrete d-dimensional torus of large side length N by the Gaussian free field on Z(d), valid in boxes of roughly side length N - N-delta with delta is an element of (1/2, 1). As an implication, the level sets of the zero-average Gaussian free field on the torus can be approximated by the level sets of the Gaussian free field on Z(d). This leads to a series of applications related to level-set percolation. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free