Truncation of long-range percolation models with square non-summable interactions

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-09-28 DOI:10.30757/alea.v19-41

Alberto M. Campos, B. D. Lima

引用次数: 1

Abstract

We consider some problems related to the truncation question in long-range percolation. It is given probabilities that certain long-range oriented bonds are open; assuming that this probabilities are not summable, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. This question is still open if the set of vertices is $\Z^2$. We give some conditions in which the answer is affirmative. One of these results generalize the previous result in [Alves, Hilario, de Lima, Valesin, Journ. Stat. Phys. {\bf 122}, 972 (2017)].

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具有平方不可和相互作用的远程渗流模型的截断

我们考虑了与长程渗流截断问题有关的一些问题。给出了某些长程定向债券是开放的概率；假设这些概率是不可求和的，当我们截断图时，我们会问渗流的概率是否为正，不允许范围超过可能很大但有限的阈值的键。如果顶点集为$\Z^2$，则此问题仍然存在。我们给出了一些答案是肯定的条件。其中一个结果推广了[Alves，Hilario，de Lima，Valesin，Journ.Stat.Phys.｛\bf 122｝，972（2017）]中的先前结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.