High-dimensional asymptotics for percolation of Gaussian free field level sets

被引：14

作者：

Drewitz, Alexander ^{[1
]}

Rodriguez, Pierre-Francois ^{[2
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2015年 / 20卷

关键词：

Gaussian free field; percolation; level sets; long-range dependence; decoupling inequalities; high dimensions; STRONGLY CORRELATED SYSTEMS; RANDOM INTERLACEMENTS; ISOPERIMETRIC-INEQUALITIES; VACANT SET;

D O I：

10.1214/EJP.v20-3416

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 consider the Gaussian free field on Z(d), d >= 3, and prove that the critical density for percolation of its level sets behaves like 1/d(1+o(1)) as d tends to infinity. Our proof gives the principal asymptotic behavior of the corresponding critical level h(*) (d). Moreover, it shows that a related parameter h(**) (d) >= h(*) (d) introduced by Rodriguez and Sznitman in [24] is in fact asymptotically equivalent to h(*) (d).

引用

页码：1 / 39

页数：39