多项式增长图渗流的局部性

IF 0.5 4区 数学 Q4 STATISTICS & PROBABILITY Electronic Communications in Probability Pub Date : 2022-05-20 DOI:10.1214/22-ecp508
D. Contreras, S'ebastien Martineau, V. Tassion
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引用次数: 5

摘要

Schramm的局部性猜想断言,满足$p_c<1$的图的临界渗流参数$p_c$的值仅取决于其局部结构。在这个注记中,我们在具有多项式增长的传递图的特殊情况下证明了这个猜想。我们的证明依赖于最近两篇关于这类图的著作,即同一作者的超临界渗流锐度和Tessera和Tointon的有限结构定理。
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Locality of percolation for graphs with polynomial growth
Schramm's Locality Conjecture asserts that the value of the critical percolation parameter $p_c$ of a graph satisfying $p_c<1$ depends only on its local structure. In this note, 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.
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来源期刊
Electronic Communications in Probability
Electronic Communications in Probability 工程技术-统计学与概率论
CiteScore
1.00
自引率
0.00%
发文量
38
审稿时长
6-12 weeks
期刊介绍: The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.
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