English

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

R2 v1 2026-06-23T12:11:22.577Z