A Markov process for a continuum infinite particle system with attraction*
Kozitsky, Yuri
Kozitsky
Yuri
Röckner, Michael
Röckner
Michael
An infinite system of point particles placed in Rd is studied. The particles are of two types; they perform random walks in the course of which those of distinct type repel each other. The interaction of this kind induces an effective multi-body attraction of the same type particles, which leads to the multiplicity of states of thermal equilibrium in such systems. The pure states of the system are locally finite counting measures on Rd. The set of such states Gamma 2 is equipped with the vague topology and the corresponding Borel sigma-field. For a special class Pexp of probability measures defined on Gamma 2, we prove the existence of a family {Pt,mu : t >= 0, mu is an element of Pexp} of probability measures defined on the space of cadlag paths with values in Gamma 2, which is a unique solution of the restricted martingale problem for the mentioned stochastic dynamics. Thereby, the corresponding Markov process is specified.
28
1-59
1-59
Institute of Mathematical Statistics (IMS)
2023