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Fluctuations for Kawasaki Dynamics

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Abstract

In this paper Kawasaki dynamics are considered. Lower bounds are obtained for the variance of the occupation time of a site in any dimension and for temperature above critical temperature. These lower bounds are expressed in terms of the density correlation function and hence relate the fluctuations to some phase transition quantities. At critical temperature, under a reasonable assumption of the static structure function, lower bounds for the variance of the occupation time are obtained. These lower bounds are consistent with the supposed value of the critical exponent. This paper also examines the same problem for Glauber dynamics and shows that the phase transition may not be of importance for the behavior of fluctuations.

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  1. Dèpartement de Mathèmatiques, Ecole Normale Supèrieure de Cachan, 61 avenue du Prèsident Wilson, 94235, Cachan, Cedex, France

    Cèdric Bernardin

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  1. Cèdric Bernardin
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Correspondence to Cèdric Bernardin.

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Bernardin, C. Fluctuations for Kawasaki Dynamics. J Stat Phys 119, 827–852 (2005). https://doi.org/10.1007/s10955-005-3769-7

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  • DOI: https://doi.org/10.1007/s10955-005-3769-7

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