Polynomial lower bound on the effective resistance for the one‐dimensional critical long‐range percolation

IF 3.1 1区数学 Q1 MATHEMATICS Communications on Pure and Applied Mathematics Pub Date : 2025-01-27 DOI:10.1002/cpa.22243

Jian Ding, Zherui Fan, Lu‐Jing Huang

引用次数: 0

Abstract

In this work, we study the critical long‐range percolation (LRP) on , where an edge connects and independently with probability 1 for and with probability for some fixed . Viewing this as a random electric network where each edge has a unit conductance, we show that with high probability the effective resistances from the origin 0 to and from the interval to (conditioned on no edge joining and ) both have a polynomial lower bound in . Our bound holds for all and thus rules out a potential phase transition (around ) which seemed to be a reasonable possibility.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

求助全文

约1分钟内获得全文去求助

来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.