First passage percolation on the exponential of two-dimensional branching random walk

被引：5
|
作者：
Ding, Jian [1 ]
Goswami, Subhajit [2 ]
机构：
[1] Univ Penn, Philadelphia, PA 19104 USA
[2] Inst Hautes Etud Sci, Paris, France
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2017年 / 22卷
关键词：
first passage percolation (FPP); branching random walk (BRW); Gaussian free field (GFF); Liouville quantum gravity (LQG);
D O I：
10.1214/17-ECP102
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 branching random walk {R-z(N) : z is an element of V-N} with Gaussian increments indexed over a two-dimensional box V-N of side length N, and we study the first passage percolation where each vertex is assigned weight e(z)(gamma R)(N) for gamma > 0. We show that for gamma > 0 sufficiently small but fixed, the expected FPP distance between the left and right boundaries is at most O (N1-gamma 2/10).
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收藏
页数：14
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