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

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

2011-08-05

arxiv.org/abs/1108.1258v1

Mathematics

Probability

24 pages, 4 figures

Scientific paper

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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