Liouville first passage percolation: geodesic length exponent is strictly larger than 1 at high temperatures
成果类型：
Article
署名作者：
Ding, Jian; Zhang, Fuxi
署名单位：
University of Chicago; Peking University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-019-00905-5
发表日期：
2019
页码：
335-367
关键词：
摘要：
Let {(v):vVN} be a discrete Gaussian free field in a two-dimensional box VN of side length N with Dirichlet boundary conditions. We study the Liouville first passage percolation, i.e., the shortest path metric where each vertex is given a weight of e(v) for some >0. We show that for sufficiently small but fixed >0, with probability tending to 1 as N, all geodesics between vertices of macroscopic Euclidean distances simultaneously have (the conjecturally unique) length exponent strictly larger than 1.
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