On Long Range Percolation with Heavy Tails

2004/09/14 by Sacha Friedli, Friedli, S., Bernardo N. B. de Lima +3
Mathematics · Physics and Astronomy · #60K35 #82B44 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.math/0409225

openalex publication_date 2004/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider independent long range percolation on Z², where horizontal and vertical edges of length n are open with probability p_n. We show that if \limsup_n→∞p_n>0, then there exists an integer N such that P_N(0↔ ∞)>0, where P_N is the truncated measure obtained by taking p_N,n=p_n for n ≤ N and p_N,n=0 for all n> N.

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