PERCOLATION FOR LEVEL-SETS OF GAUSSIAN FREE FIELDS ON METRIC GRAPHS

被引：12

作者：

Ding, Jian ^{[1
]}

Wirth, Mateo ^{[1
]}

机构：

[1] Univ Penn, Dept Stat, Philadelphia, PA 19104 USA

来源：

ANNALS OF PROBABILITY | 2020年 / 48卷 / 03期

关键词：

Gaussian free field; percolation; chemical distance; phase transition; metric graph; RANDOM INTERLACEMENTS; CLUSTERS;

D O I：

10.1214/19-AOP1397

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity and is sharp up to a poly-logarithmic factor with an exponent of one-quarter. This substantially improves a previous result by Li and the first author. In three dimensions and higher, we provide rather precise estimates of percolation probabilities in different regimes which altogether describe a sharp phase transition.

引用

页码：1411 / 1435

页数：25

共 22 条

[1]

[Anonymous], 1999, Fundamental Principles of Mathematical Sciences

[2]

ARU J., ARX2V17060773737

[3]

ARU J., ARX2V180509204

[4] Kesten's incipient infinite cluster and quasi-multiplicativity of crossing probabilities [J].