Percolation of even sites for random sequential adsorption

TL;DR

This paper investigates the percolation threshold in a red/blue chequerboard lattice under random sequential adsorption, establishing that the critical blue arrival rate for infinite connectivity exceeds one.

Contribution

It proves that the critical blue arrival rate for percolation is finite and strictly greater than one, providing new insights into percolation thresholds in such lattice models.

Findings

Critical blue rate for percolation is finite.

Critical blue rate exceeds one.

Infinite blue component occurs above this threshold.

Abstract

Consider random sequential adsorption on a red/blue chequerboard lattice with arrivals at rate $1$ on the red squares and rate $\lambda$ on the blue squares. We prove that the critical value of $\lambda$, above which we get an infinite blue component, is finite and strictly greater than $1$.