Critical site percolation in high dimension

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.

arXiv comment30 pages. Presentation revised

References in corpus (5)

• Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk
• Series Expansion of the Percolation Threshold on Hypercubic Lattices
• Mean-field behavior for nearest-neighbor percolation in $d>10$
• Expansion in $n^{-1}$ for percolation critical values on the $n$-cube and $Z^n$: the first three terms
• Expansion for the critical point of site percolation: the first three terms

Cited by in corpus (1)

• A branching process with deletions and mergers that matches the threshold for hypercube percolation