RECURRENCE OF THE UNIFORM INFINITE HALF-PLANE MAP VIA DUALITY OF RESISTANCES
成果类型：
Article
署名作者：
Budzinski, Thomas; Lehericy, Thomas
署名单位：
Ecole Normale Superieure de Lyon (ENS de LYON); University of Zurich
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/21-AOP1539
发表日期：
2022
页码：
1725-1754
关键词：
摘要：
We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that the simple random walk is recurrent, and that the resistance between the root and the boundary of the hull of radius r is at least of order log r . This resistance bound is expected to be sharp, and is better than those following from previous proofs of recurrence for nonbounded-degree planar maps models. Our main tools are the self-duality of uniform planar maps, a classical lemma about duality of resistances and some peeling estimates. The proof shares some ideas with Russo-Seymour-Welsh theory in percolation.