Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation

2024/04/10 by Tom Hutchcroft, Hutchcroft, Tom · 2 citations
Mathematics · #Stochastic processes and statistical mechanics #Random Matrices and Applications #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2404.07276

Abstract

In long-range percolation on ℤ^d, we connect each pair of distinct points x and y by an edge independently at random with probability 1-exp(-β‖x-y‖^-d-α), where α>0 is fixed and β≥ 0 is a parameter. In a previous paper, we proved that if 0<α

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