Brownian web in the scaling limit of supercritical oriented percolation in dimension 1 + 1

Anish Sarkar (Indian Statistical Institute, New Delhi)
Rongfeng Sun (National University of Singapore)

Abstract


We prove that, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2_{even}:={(x,i) in Z^2: x+i is even} converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect.

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Pages: 1-23

Publication Date: February 5, 2013

DOI: 10.1214/EJP.v18-2019

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