论文标题
Markov的过程，用于具有吸引力的连续无限粒子系统
A Markov process for a continuum infinite particle system with attraction
论文作者
论文摘要
研究了一个放置在$ \ mathds {r}^d $中的无限点粒子系统。颗粒有两种类型。他们在那些不同类型的过程中进行随机步行。这种相互作用引起了同一类型粒子的有效多体吸引力，从而导致此类系统中热平衡状态的多样性。系统的纯状态是$ \ mathds {r}^d $上的本地有限计数措施。此类状态的集合$γ^2 $配备了模糊的拓扑结构和相应的Borel $σ$ - 场。对于特殊类$ \ Mathcal {p} _ {\ rm Exp} $的概率度量$ c {à} dl {à} g路径带有$γ^2 $中的值，这是上述随机动力学的限制性martingale问题的独特解决方案。因此，指定了相应的马尔可夫进程。
An infinite system of point particles placed in $\mathds{R}^d$ is studied. The particles are of two types; they perform random walks in the course of which those of distinct types 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 $\mathds{R}^d$. The set of such states $Γ^2$ is equipped with the vague topology and the corresponding Borel $σ$-field. For a special class $\mathcal{P}_{\rm exp}$ of probability measures defined on $Γ^2$, we prove the existence of a family $\{P_{t,μ}: t\geq 0, \ μ\in \mathcal{P}_{\rm exp}\}$ of probability measures defined on the space of c{à}dl{à}g paths with values in $Γ^2$, which is a unique solution of the restricted martingale problem for the mentioned stochastic dynamics. Thereby, the corresponding Markov process is specified.
