Families of Vicious Walkers

Details Families of Vicious Walkers Families of Vicious Walkers

2002-08-12

arxiv.org/abs/cond-mat/0208228v2

J. Phys. A, 36, 609, 2003.

Physics

Condensed Matter

Statistical Mechanics

20 pages, 5 figures. v.2: minor additions and corrections

Scientific paper

10.1088/0305-4470/36/3/302

We consider a generalisation of the vicious walker problem in which N random walkers in R^d are grouped into p families. Using field-theoretic renormalisation group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t. For d>2, this is constant, but for d<2 it decays as a power t^(-alpha), which we compute to O(epsilon^2) in an expansion in epsilon=2-d. The second order term depends on the ratios of the diffusivities of the different families. In two dimensions, we find a logarithmic decay (ln t)^(-alpha'), and compute alpha' exactly.

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