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2013 Brownian web in the scaling limit of supercritical oriented percolation in dimension 1 + 1
Anish Sarkar, Rongfeng Sun
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Electron. J. Probab. 18: 1-23 (2013). DOI: 10.1214/EJP.v18-2019

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 $Z^2_{\mathrm{even}}:=\{(x,i) in Z^2: x+i \mathrm{is even}\}$ 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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Anish Sarkar. Rongfeng Sun. "Brownian web in the scaling limit of supercritical oriented percolation in dimension 1 + 1." Electron. J. Probab. 18 1 - 23, 2013. https://doi.org/10.1214/EJP.v18-2019

Information

Accepted: 5 February 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1290.60107
MathSciNet: MR3035749
Digital Object Identifier: 10.1214/EJP.v18-2019

Subjects:
Primary: 60K35
Secondary: 82B43

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Vol.18 • 2013
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