Locality of percolation for graphs with polynomial growth

被引：2

作者：

Contreras, Daniel ^{[1
]}

Martineau, Sebastien ^{[2
]}

Tassion, Vincent ^{[1
]}

机构：

[1] Swiss Fed Inst Technol, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Sorbonne Univ, LPSM, 4 Pl Jussieu, F-75005 Paris, France

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2023年 / 28卷

基金：

欧盟地平线“2020”; 欧洲研究理事会;

关键词：

percolation; Schramm's Locality Conjecture; transitive graphs of polynomial growth;

D O I：

10.1214/22-ECP508

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：

Schramm's Locality Conjecture asserts that the value of the critical parameter pc of a graph satisfying pc < 1 depends only on its local structure. In this paper, we prove this conjecture in the particular case of transitive graphs with polynomial growth. Our proof relies on two recent works about such graphs, namely supercritical sharpness of percolation by the same authors and a finitary structure theorem by Tessera and Tointon.

引用

页码：1 / 9

页数：10

共 50 条

[1] SUPERCRITICAL PERCOLATION ON GRAPHS OF POLYNOMIAL GROWTH
Contreras, Daniel
Martineau, Sebastien
Tassion, Vincent
DUKE MATHEMATICAL JOURNAL, 2024, 173 (04) : 745 - 806
[2] LOCALITY OF PERCOLATION FOR ABELIAN CAYLEY GRAPHS
Martineau, Sebastien
Tassion, Vincent
ANNALS OF PROBABILITY, 2017, 45 (02): : 1247 - 1277
[3] STRICT MONOTONICITY FOR FIRST PASSAGE PERCOLATION ON GRAPHS OF POLYNOMIAL GROWTH AND QUASI-TREES
Gorski, Christian
ANNALS OF PROBABILITY, 2024, 52 (04): : 1487 - 1537
[4] Polynomial growth in degree-dependent first passage percolation on spatial random graphs
Komjathy, Julia
Lapinskas, John
Lengler, Johannes
Schaller, Ulysse
ELECTRONIC JOURNAL OF PROBABILITY, 2024, 29
[5] GRAPHS WITH POLYNOMIAL-GROWTH ARE COVERING GRAPHS
GODSIL, CD
SEIFTER, N
GRAPHS AND COMBINATORICS, 1992, 8 (03) : 233 - 241
[6] GRAPHS WITH POLYNOMIAL-GROWTH
TROFIMOV, VI
MATHEMATICS OF THE USSR-SBORNIK, 1984, 123 (3-4): : 405 - 417
[7] Approximating graphs with polynomial growth
Seifter, N
Woess, W
GLASGOW MATHEMATICAL JOURNAL, 2000, 42 : 1 - 8
[8] Lattices in graphs with polynomial growth
Lukacs, A
Seifter, N
DISCRETE MATHEMATICS, 1998, 186 (1-3) : 227 - 236
[9] Note on locality of volume growth rate of graphs
Song, He
Xiang, Kainan
STATISTICS & PROBABILITY LETTERS, 2024, 206
[10] Finite contractions of graphs with polynomial growth
Lukács, A
Seifter, N
EUROPEAN JOURNAL OF COMBINATORICS, 2001, 22 (01) : 85 - 90

← 1 2 3 4 5 →