Critical site percolation in high dimension
Probability
2020-10-28 v3
Abstract
We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field behavior in high dimensions.
Keywords
Cite
@article{arxiv.1911.04159,
title = {Critical site percolation in high dimension},
author = {Markus Heydenreich and Kilian Matzke},
journal= {arXiv preprint arXiv:1911.04159},
year = {2020}
}
Comments
30 pages. Presentation revised