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Kawasaki dynamics in the continuum via generating functionals evolution. (English) Zbl 1249.82007

The Kawasaki dynamics is an example of a hopping particle model, where particles hop randomly over the space \(\mathbb R^d\) according to a rate depending on the interaction between particles (see, for example, [Y. Kondratiev, E. Lytvynov and M. Röckner, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10, No. 2, 185–209 (2007; Zbl 1142.60064)]).
The authors construct the time evolution of Kawasaki dynamics for a spatial infinite particle systems in terms of generating functionals. This is carried out via the approach of Ovsjannikov type (using a scale of Banach spaces) leading to a solution local in time. An application to Vlasov-type scaling in terms of generating functionals is given.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
46G20 Infinite-dimensional holomorphy
46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces

Citations:

Zbl 1142.60064
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