Diffusive behaviour of the equilibrium fluctuations in the asymmetric exclusion processes. (English) Zbl 1080.60094

Funaki, Tadahisa (ed.) et al., Stochastic analysis on large scale interacting systems. Papers from the 11th international conference, Hayama, Japan, July 17–26, 2002 and the international conference on stochastic analysis and statistical mechanics, Kyoto, Japan, July 29–30, 2002. Tokyo: Mathematical Society of Japan (ISBN 4-931469-24-8/hbk). Advanced Studies in Pure Mathematics 39, 307-324 (2004).
For the case of two classes of particles the paper gives a simple proof of the infinite volume behaviour of the asymmetric exclusion process in \(d \geq 3\) which is based on the fluctuation-dissipation theorem stated by the same authors. The later theorem is proved due to a specific duality of the model. The authors claim that there are no results of this type for systems that do not have such nice duality.
For the entire collection see [Zbl 1050.60001].


60K35 Interacting random processes; statistical mechanics type models; percolation theory