A Markov process for a continuum infinite particle system with attraction.
A talk in the Bielefeld Stochastic Afternoon series by
Jurij Kozicki
| Abstract: | This talk will be held via Zoom (for details email stochana(at)math.uni-bielefeld.de). An infinite system of point particles placed in $\mathbb{R}^d$ is studied. The particles are of two types; they perform random walks (jumps) in the course of which those of distinct types repel each other. This interaction induces effective attraction of the same type particles, which leads to the multiplicity of sates of thermal equilibrium in such systems. The pure states of the system are locally finite subsets of $\mathbb{R}^d$, which can also be interpreted as locally finite counting measures. For a special class $\mathcal{P}_{exp}$ of (sub-Poissnian) probability measures on the set of pure states, we prove the existence of a unique family $\{P_{t,\mu}: t\geq 0, \ \mu \in \mathcal{P}_{exp}\}$ of probability measures on the space of cádlág paths which solves a martingale problem for the mentioned system. Thereby, a Markov process with cádlág paths is specified which describes the stochastic dynamics of this particle system. Joint work with Michael Roeckner Within the CRC this talk is associated to the project(s): A5 |