منابع مشابه
Lattice paths: vicious walkers and friendly walkers
In an earlier paper [4] the problem of vicious random walkers on a d-dimensional directed lattice was considered. \Vicious walkers" describes the situation in which two or more walkers arriving at the same lattice site annihilate one another. Accordingly, the only allowed con gurations are those in which contacts are forbidden. Alternatively expressed as a static rather than dynamic problem, vi...
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We consider a generalisation of the vicious walker problem in which N random walkers in R 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, which we compute to O(ε) in an...
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We propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for m particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-d...
متن کاملA Reflection Principle for Three Vicious Walkers
We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of the configurations of three vicious walkers to that of configurations of two vicious walkers. In the combinatorial treatment of two vicious walkers, we make connections to two-chain watermelons and to the classical ballot problem. Precisely, the reflection principle leads to a bijec...
متن کاملFunctional central limit theorems for vicious walkers
We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval (0, T ] for the first type and in an infinite time interval (0,∞) for the second type, ...
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ژورنال
عنوان ژورنال: EPL (Europhysics Letters)
سال: 2011
ISSN: 0295-5075,1286-4854
DOI: 10.1209/0295-5075/96/50009