Non-equilibrium stochastic dynamics in continuum: The free case
| dc.creator | Kondratiev, Y. | |
| dc.creator | Lytvynov, E. | |
| dc.creator | Röckner, M. | |
| dc.date | 2007-01-25 | |
| dc.date.accessioned | 2026-07-07T07:43:02Z | |
| dc.date.available | 2026-07-07T07:43:02Z | |
| dc.description | We study the problem of identification of a proper state-space for the stochastic dynamics of free particles in continuum, with their possible birth and death. In this dynamics, the motion of each separate particle is described by a fixed Markov process $M$ on a Riemannian manifold $X$. The main problem arising here is a possible collapse of the system, in the sense that, though the initial configuration of particles is locally finite, there could exist a compact set in $X$ such that, with probability one, infinitely many particles will arrive at this set at some time $t>0$. We assume that $X$ has infinite volume and, for each $α\ge1$, we consider the set $Θ_α$ of all infinite configurations in $X$ for which the number of particles in a compact set is bounded by a constant times the $α$-th power of the volume of the set. We find quite general conditions on the process $M$ which guarantee that the corresponding infinite particle process can start at each configuration from $Θ_α$, will never leave $Θ_α$, and has cadlag (or, even, continuous) sample paths in the vague topology. We consider the following examples of applications of our results: Brownian motion on the configuration space, free Glauber dynamics on the configuration space (or a birth-and-death process in $X$), and free Kawasaki dynamics on the configuration space. We also show that if $X=\mathbb R^d$, then for a wide class of starting distributions, the (non-equilibrium) free Glauber dynamics is a scaling limit of (non-equilibrium) free Kawasaki dynamics. | |
| dc.identifier | https://arxiv.org/abs/math/0701736 | |
| dc.identifier | http://arxiv.org/abs/math/0701736 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122668 | |
| dc.subject | Probability | |
| dc.subject | 60K35, 60J65, 60J75, 60J80, 82B21 | |
| dc.title | Non-equilibrium stochastic dynamics in continuum: The free case | |
| dc.type | text |