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

2020/09/28 by Alberto M. Campos, Campos, Alberto M., Bernardo N. B. de Lima +1
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2009.13671

Abstract

We consider some problems related to the truncation question in long-range\npercolation. It is given probabilities that certain long-range oriented bonds\nare open; assuming that this probabilities are not summable, we ask if the\nprobability of percolation is positive when we truncate the graph, disallowing\nbonds of range above a possibly large but finite threshold. This question is\nstill open if the set of vertices is Z². We give some conditions in which\nthe answer is affirmative. One of these results generalize the previous result\nin [Alves, Hil 'ario, de Lima, Valesin, Journ. Stat. Phys. bf 122, 972\n(2017)].\n

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