Perturbations of supercritical oriented percolation and sticky Brownian webs
Probability
2019-10-25 v2
Abstract
Previously, Sarkar and Sun have shown that for supercritical oriented percolation in dimension , the set of rightmost infinite open paths converges to the Brownian web after proper centering and scaling. In this note, we show that a pair of sticky Brownian webs arise naturally if one considers the set of right-most infinite open paths for two coupled percolation configurations with distinct (but close) percolation parameters. This leads to a natural conjecture on the convergence of the dynamical supercritical oriented percolation model to the so-called dynamical Brownian web.
Cite
@article{arxiv.1811.01849,
title = {Perturbations of supercritical oriented percolation and sticky Brownian webs},
author = {Emmanuel Schertzer and Rongfeng Sun},
journal= {arXiv preprint arXiv:1811.01849},
year = {2019}
}