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29 March 2024
 
  » arxiv » math.PR/0410181

 Article overview


On diffusivity of a tagged particle in asymmetric zero-range dynamics
Sunder Sethuraman ;
Date 6 Oct 2004
Subject Probability MSC-class: 60K35 | math.PR
AbstractConsider a tagged particle in zero-range dynamics on the integer lattice in dimension d with rate g whose finite-range jump probabilities p possess a drift. We show, in equilibrium, that the variance of the tagged particle position at time t is at least order t in all dimensions and at most order t in d=1 and d larger or equal to 3 for a wide class of rates g. Also, in d=1, when the jump distribution p is totally asymmetric and nearest-neighbor, and when the rate g(k) increases and g(k)/k decreases with k, we show the diffusively scaled centered tagged particle position converges to a Brownian motion.
Source arXiv, math.PR/0410181
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