An upper bound for $p_c$ in range-$R$ bond percolation in two and three dimensions
Probability
2021-07-30 v1
Abstract
An upper bound for the critical probability of long range bond percolation in and is obtained by connecting the bond percolation with the SIR epidemic model, thus complementing the lower bound result in Frei and Perkins arXiv:arch-ive/1603.04130. A key ingredient is that we establish a uniform bound for the local times of branching random walk by calculating their exponential moments and by using the discrete versions of Tanaka's formula and Garsia's Lemma.
Keywords
Cite
@article{arxiv.2107.14173,
title = {An upper bound for $p_c$ in range-$R$ bond percolation in two and three dimensions},
author = {Jieliang Hong},
journal= {arXiv preprint arXiv:2107.14173},
year = {2021}
}