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Entropy Analysis of a Nearest-Neighbor Attractive/Repulsive Exclusion Process on One-Dimensional Lattices

Hirotake Yaguchi
The Annals of Probability
Vol. 18, No. 2 (Apr., 1990), pp. 556-580
Stable URL: http://www.jstor.org/stable/2244303
Page Count: 25
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Entropy Analysis of a Nearest-Neighbor Attractive/Repulsive Exclusion Process on One-Dimensional Lattices
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Abstract

Stationary measures for an interactive exclusion process on Z are considered. The process is such that the jump rate of each particle to the empty neighboring site is $\alpha > 0$ (resp., $\beta > 0$) when another neighboring site is occupied (resp., unoccupied) by a particle, and that α ≠ β. According as $\alpha < \beta$ or $\alpha > \beta$ the process becomes nearest-neighbor attractive or repulsive, respectively. The method of relative entropy is used to determine the family Mβ/α of stationary measures. The member of Mγ is simply described as the probability measure having the regular clustering property which is a generalization of the exchangeable property of measures. It is shown that extremal points of Mγ are renewal measures. Thus the structure of stationary measures for the process is completely determined.

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