Truncation of long-range percolation model with square non-summable interactions
Probability
2022-07-21 v2
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 . 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)].
Keywords
Cite
@article{arxiv.2009.13671,
title = {Truncation of long-range percolation model with square non-summable interactions},
author = {Alberto M. Campos and Bernardo N. B. de Lima},
journal= {arXiv preprint arXiv:2009.13671},
year = {2022}
}