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

In this work, we study the critical long‐range percolation (LRP) on Z$\mathbb {Z}$, where an edge connects i$i$ and j$j$ independently with probability 1 for |i−j|=1$|i-j|=1$ and with probability 1−exp{−β∫ii+1∫jj+1|u−v|−2dudv}$1-\exp \lbrace -\beta \int _i^{i+1}\int _j^{j+1}|u-v|^{-2}{\rm d}u{\rm d}...

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Bibliographic Details

Published in:	Communications on pure and applied mathematics Vol. 78; no. 7; pp. 1251 - 1284
Main Authors:	Ding, Jian, Fan, Zherui, Huang, Lu‐Jing
Format:	Journal Article
Language:	English
Published:	New York John Wiley and Sons, Limited 01.07.2025
Subjects:	Electrical networks Lower bounds Percolation Phase transitions Polynomials
ISSN:	0010-3640, 1097-0312
Online Access:	Get full text
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