Dresden 2006 – wissenschaftliches Programm

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AKB: Biologische Physik

AKB 17: Population Dynamics

AKB 17.3: Vortrag

Mittwoch, 29. März 2006, 15:00–15:15, ZEU 260

Vicious walkers in one-body potentials — •Karen Winkler¹ and Alan J. Bray² — ¹Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center of Nanoscience (CeNS), LMU München — ²Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, U.K.

Vicious walkers are short-ranged interacting random walkers which annihilate each other on meeting. The backward Fokker-Planck equation is an elegant tool to derive the asymptotic behavior of the probability that all N vicious walkers have survived. We introduce a method to compute the survival probability of N vicious walkers in general one-body potentials. Using this method we are able to give results for N vicious walkers on a semi-infinite line with reflecting boundary at the origin [1].
We also derive explicit results for three vicious walkers in an inverted harmonic potential, which can be interpreted as a new predator-prey problem [2].

[1] A.J. Bray and K. Winkler, J. Phys. A 37,5493 (2004)

[2] K. Winkler and A.J. Bray, J. Stat. Mech.(2005) PO2005