Front propagation in an exclusion one-dimensional reactive dynamics
| dc.creator | Jara, Milton | |
| dc.creator | Moreno, Gregorio | |
| dc.creator | Ramirez, Alejandro F. | |
| dc.date | 2007-03-06 | |
| dc.date.accessioned | 2026-07-07T07:50:28Z | |
| dc.date.available | 2026-07-07T07:50:28Z | |
| dc.description | We consider an exclusion process representing a reactive dynamics of a pulled front on the integer lattice, describing the dynamics of first class $X$ particles moving as a simple symmetric exclusion process, and static second class $Y$ particles. When an $X$ particle jumps to a site with a $Y$ particle, their position is intechanged and the $Y$ particle becomes an $X$ one. Initially, there is an arbitrary configuration of $X$ particles at sites $..., -1,0$, and $Y$ particles only at sites $1,2,...$, with a product Bernoulli law of parameter $ρ,0<ρ<1$. We prove a law of large numbers and a central limit theorem for the front defined by the right-most visited site of the $X$ particles at time $t$. These results corroborate Monte-Carlo simulations performed in a similar context. We also prove that the law of the $X$ particles as seen from the front converges to a unique invariant measure. The proofs use regeneration times: we present a direct way to define them within this context. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703173 | |
| dc.identifier | http://arxiv.org/abs/math/0703173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125175 | |
| dc.subject | Probability | |
| dc.subject | 60F17; 82C22 | |
| dc.title | Front propagation in an exclusion one-dimensional reactive dynamics | |
| dc.type | text |