The semigroup of the Glauber dynamics of a continuous system of free particles
| dc.creator | Kondratiev, Yuri | |
| dc.creator | Lytvynov, Eugene | |
| dc.creator | Röckner, Michael | |
| dc.date | 2004-07-21 | |
| dc.date.accessioned | 2026-07-07T05:10:32Z | |
| dc.date.available | 2026-07-07T05:10:32Z | |
| dc.description | We study properties of the semigroup $(e^{-tH})_{t\ge 0}$ on the space $L^ 2(Γ_X,π)$, where $Γ_X$ is the configuration space over a locally compact second countable Hausdorff topological space $X$, $π$ is a Poisson measure on $Γ_X$, and $H$ is the generator of the Glauber dynamics. We explicitly construct the corresponding Markov semigroup of kernels $(P_t)_{t\ge 0}$ and, using it, we prove the main results of the paper: the Feller property of the semigroup $(P_t)_{t\ge 0}$ with respect to the vague topology on the configuration space $Γ_X$, and the ergodic property of $(P_t)_{t\ge 0}$. Following an idea of D. Surgailis, we also give a direct construction of the Glauber dynamics of a continuous infinite system of free particles. The main point here is that this process can start in every $γ\inΓ_X$, will never leave $Γ_X$ and has cadlag sample paths in $Γ_X$. | |
| dc.identifier | https://arxiv.org/abs/math/0407359 | |
| dc.identifier | http://arxiv.org/abs/math/0407359 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71955 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35; 60J75; 60J80; 82C21 | |
| dc.title | The semigroup of the Glauber dynamics of a continuous system of free particles | |
| dc.type | text |