Seminar at SMU Delhi
April 18, 2012 (Wednesday) ,
3:30 PM at Webinar
Indian Statistical Institute, Delhi
Brownian Web in the Scaling Limit of Supercritical Oriented Percolation in Dimension 1 + 1
Abstract of Talk
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 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 distinct exploration clusters evolve independently before they intersect.