On diffusivity of a tagged particle in asymmetric zero-range dynamics
نویسنده
چکیده
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 jp(j) 6= 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 also 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. Abbreviated title: On diffusivity of a tagged particle in zero-range. AMS (2000) subject classifications: Primary 60K35; secondary 60F05.
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