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

Alberto M. Campos; Bernardo N. B. de Lima

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arXiv · 2009.13671

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

Alberto M. Campos·Bernardo N. B. de Lima

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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, Hil\'ario, de Lima, Valesin, Journ. Stat. Phys. {\bf 122}, 972 (2017)].

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Alberto M. Campos, Bernardo N. B. de Lima. 2020-09-28. Truncation of long-range percolation model with square non-summable interactions. https://arxiv.org/abs/2009.13671

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