Asymptotic expansion of the critical point for oriented percolation in high dimensions

TL;DR

This paper derives an asymptotic expansion for the critical point of high-dimensional oriented percolation using lace expansion, providing insights into the behavior as dimension grows large.

Contribution

It introduces a novel asymptotic expansion of the critical point for oriented percolation in high dimensions, expanding understanding of percolation thresholds.

Findings

Asymptotic expansion of the critical point in powers of 1/d

Application of lace expansion techniques

Results valid as dimension approaches infinity

Abstract

We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on $\mathbb Z^d$ in powers of $d^{-1}$ as $d\rightarrow \infty$. The proof relies heavily on the lace expansion.