Continuous first-passage percolation and continuous greedy paths model: linear growth

TL;DR

This paper investigates a continuous first-passage percolation model on , analyzing conditions under which the infected region grows linearly by comparing it with a continuous greedy paths model.

Contribution

It establishes criteria for linear growth in a continuous percolation model by adapting results from lattice-based greedy path models.

Findings

Identifies conditions for linear growth in the continuous model

Connects continuous growth behavior to lattice greedy path results

Provides a framework for analyzing growth in continuous percolation models

Abstract

We study a random growth model on $\R^d$ introduced by Deijfen. This is a continuous first-passage percolation model. The growth occurs by means of spherical outbursts with random radii in the infected region. We aim at finding conditions on the distribution of the random radii to determine whether the growth of the process is linear or not. To do so, we compare this model with a continuous analogue of the greedy lattice paths model and transpose results in the lattice setting to the continuous setting.