Families of vicious walkers
Abstract
We consider a generalization of the vicious walker problem in which N random walkers in R^{d} are grouped into p families. Using fieldtheoretic renormalization 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 Script O(varepsilon^{2}) in an expansion in varepsilon = 2  d. The secondorder term depends on the ratios of the diffusivities of the different families. In two dimensions, we find a logarithmic decay (ln t)^{bar alpha} and compute bar alpha exactly.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2003
 DOI:
 10.1088/03054470/36/3/302
 arXiv:
 arXiv:condmat/0208228
 Bibcode:
 2003JPhA...36..609C
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 20 pages, 5 figures. v.2: minor additions and corrections