On diffusivity of a tagged particle in asymmetric zero-range dynamics

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6 Scopus citations

Abstract

Consider a distinguished, or tagged particle in zero-range dynamics on Zd with rate g whose finite-range jump probabilities p possess a drift ∑ j p (j) ≠ 0. We show, in equilibrium, that the variance of the tagged particle position at time t is at least order t in all d ≥ 1, and at most order t in d = 1 and d ≥ 3 for a wide class of rates g. Also, in d = 1, when the jump distribution p is totally asymmetric and nearest-neighbor, and the rate g (k) increases, and g (k) / k either decreases or increases with k, we show the diffusively scaled centered tagged particle position converges to a Brownian motion with a homogenized diffusion coefficient in the sense of finite-dimensional distributions. Some characterizations of the tagged particle variance are also given.

Original languageEnglish (US)
Pages (from-to)215-232
Number of pages18
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume43
Issue number2
DOIs
StatePublished - Mar 2007

Keywords

  • Diffusive
  • Invariance principle
  • Tagged particle
  • Variance
  • Zero-range

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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