Electronic Journal of Probability

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

Anish Sarkar and Rongfeng Sun

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 21, 23 pp.

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

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]

Brownian web oriented percolation

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Sarkar, Anish; Sun, Rongfeng. Brownian web in the scaling limit of supercritical oriented percolation in dimension 1 + 1. Electron. J. Probab. 18 (2013), paper no. 21, 23 pp. doi:10.1214/EJP.v18-2019. https://projecteuclid.org/euclid.ejp/1465064246

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