Families of Vicious Walkers
arXiv:cond-mat/0208228 · doi:10.1088/0305-4470/36/3/302
Abstract
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.
20 pages, 5 figures. v.2: minor additions and corrections
References in corpus (1)
Cited by in corpus (22)
- Persistence and First-Passage Properties in Non-equilibrium Systems
- Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
- Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
- Maximum distributions of bridges of noncolliding Brownian paths
- Persistence properties of a system of coagulating and annihilating random walkers
- First-Passage Exponents of Multiple Random Walks
- Ordering of Random Walks: The Leader and the Laggard
- Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers
- Kinetics of First Passage in a Cone
- O'Connell's process as a vicious Brownian motion
- Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process
- Survival probability of mutually killing Brownian motions and the O'Connell process
- Vicious Lévy flights
- On the Mixing of Diffusing Particles
- Vicious walks with long-range interactions
- Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey
- Moments of vicious walkers and Möbius graph expansions
- Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts
- First Passage in Infinite Paraboloidal Domains
- Diffusion in a fluid flow generated by a source at the apex of a wedge
- Infinite System of Random Walkers: Winners and Losers
- Determinantal Martingales and Correlations of Noncolliding Random Walks