A lower bound for $p_c$ in range-$R$ bond percolation in two and three dimensions
Probability
2016-03-15 v1
Abstract
We use the connection between bond percolation and SIR epidemics to establish lower bounds for the critical percolation probability in and dimensions as the range becomes large. The bound agrees with the conjectured asymptotics for the long range critical probability, refines results of M. Penrose, and complements results of van der Hofstad and Sakai in dimensions greater than .
Keywords
Cite
@article{arxiv.1603.04130,
title = {A lower bound for $p_c$ in range-$R$ bond percolation in two and three dimensions},
author = {Spencer Frei and Edwin Perkins},
journal= {arXiv preprint arXiv:1603.04130},
year = {2016}
}