TY - JOUR

T1 - On diffusivity of a tagged particle in asymmetric zero-range dynamics

AU - Sethuraman, Sunder

N1 - Funding Information:
* Tel.: +(515) 294 8140; fax: +(515) 294 5454. E-mail address: sethuram@iastate.edu (S. Sethuraman). 1 Research supported in part by NSA-H982300510041 and NSF/DMS-0504193.

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

KW - Diffusive

KW - Invariance principle

KW - Tagged particle

KW - Variance

KW - Zero-range

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U2 - 10.1016/j.anihpb.2006.03.002

DO - 10.1016/j.anihpb.2006.03.002

M3 - Article

AN - SCOPUS:33847266293

SN - 0246-0203

VL - 43

SP - 215

EP - 232

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 2

ER -