Vicious accelerating walkers

S. L.Y. Xu, J. M. Schwarz

Research output: Contribution to journalArticlepeer-review


A vicious-walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to the position. We numerically compute the survival probability exponent, α, for this system, which characterizes the probability for any two walkers not to meet. For example, for N=3, α=0.710.01. Based on our numerical data, we conjecture that is an upper bound on α. We also numerically study N vicious Levy flights and find, for instance, for N=3 and a Levy index μ=1 that α=1.310.03. Vicious accelerating walkers relate to no-crossing configurations of semiflexible polymer brushes and may prove relevant for a non-Markovian extension of Dyson's Brownian motion model.

Original languageEnglish (US)
Article number50009
Issue number5
StatePublished - Dec 2011

ASJC Scopus subject areas

  • General Physics and Astronomy


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