Theoretical Statistics and Mathematics Unit, ISI Delhi

Brownian Web in the Scaling Limit of Supercritical Oriented Percolation in Dimension $1+1$

by Anish Sarkar and Rongfeng Sun

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 $\Z^2_{\rm even}:=\{(x,i)\in \Z^2: x+i \mbox{ is even}\}$ 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.

isid/ms/2011/11 [fulltext]

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