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The Brownian net

Research paper by Rongfeng Sun, Jan M. Swart

Indexed on: 13 Jun '08Published on: 13 Jun '08Published in: Mathematics - Probability



Abstract

The (standard) Brownian web is a collection of coalescing one- dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net, and study some of its elementary properties.