Collision probability for random trajectories in two dimensions

A. Gaudillière

Stochastic Processes and their Applications, 2009, vol. 119, issue 3, 775-810

Abstract: We give a lower bound for the non-collision probability up to a long time T in a system of n independent random walks with fixed obstacles on . By 'collision' we mean collision between the random walks as well as collision with the fixed obstacles. We give an analogous result for Brownian particles on the plane. As a corollary we show that the non-collision request leads only to logarithmic corrections for a spread-out property of the independent random walk system.

Keywords: Non-collision; probability; Potential; theory; Scale-invariance; properties; Kawasaki; dynamics (search for similar items in EconPapers)
Date: 2009
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