Year: 2026
Type: preprint
Abstract: We consider the Boolean model of continuum percolation, where points are placed in $\mathbb{R}^d$ by a Poisson point process and pairs of points with distance at most 1 are connected by an edge. The time constant is the limiting ratio of the chemical distance (i.e. graph distance) to the Euclidean distance for pairs of distant connected points. Yao, Chen, and Guo established the existence of a time constant in the supercritical regime. We show that above the critical intensity, the time constant is a Lipschitz continuous function of the intensity. The proof adapts a recent argument of Can, Nakajima, and Nguyen to the continuous setting.
Source: arXiv (Cornell University)
Authors: Dubin, Karoline, Gorski, Christian
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7163071376