Critical site percolation in high dimension

TL;DR

This paper uses advanced mathematical techniques to analyze critical site percolation in high-dimensional lattices, establishing mean-field behavior and critical exponents.

Contribution

It proves an infra-red bound and derives critical exponents for high-dimensional site percolation using the lace expansion.

Findings

Establishment of infra-red bound for high-dimensional site percolation

Verification of the triangle condition in high dimensions

Derivation of critical exponents indicating mean-field behavior

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.