Expansion for the critical point of site percolation: the first three terms

TL;DR

This paper rigorously derives the first three terms of the expansion for the critical point of site percolation on high-dimensional hypercubic lattices using the lace expansion, advancing theoretical understanding of percolation thresholds.

Contribution

It provides a rigorous derivation of the first three terms in the critical point expansion for high-dimensional site percolation, improving upon previous approximations.

Findings

First three terms of the critical point expansion obtained rigorously.

Uses lace expansion technique for high-dimensional lattices.

Enhances theoretical precision in percolation threshold estimates.

Abstract

We expand the critical point for site percolation on the $d$-dimensional hypercubic lattice in terms of inverse powers of $2d$, and we obtain the first three terms rigorously. This is achieved using the lace expansion.