Large Deviations of the Front in a one dimensional model of $X+Y \to 2X$
| dc.creator | Bérard, Jean | |
| dc.creator | Ramírez, Alejandro | |
| dc.date | 2008-07-15 | |
| dc.date.accessioned | 2026-07-07T09:50:27Z | |
| dc.date.available | 2026-07-07T09:50:27Z | |
| dc.description | We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction $X+Y \to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent simple continuous time random walks of total jump rate $2$. For a wide class of initial conditions, we prove that a large deviations principle holds and we show that the zero set of the rate function is the interval $[0,v]$, where $v$ is the velocity of the front given by the law of large numbers. We also give more precise estimates for the rate of decay of the slowdown probabilities. Our results indicate a gapless property of the generator of the process as seen from the front, as it happens in the context of nonlinear diffusion equations describing the propagation of a pulled front into an unstable state. | |
| dc.identifier | https://arxiv.org/abs/0807.2349 | |
| dc.identifier | http://arxiv.org/abs/0807.2349 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164950 | |
| dc.subject | Probability | |
| dc.title | Large Deviations of the Front in a one dimensional model of $X+Y \to 2X$ | |
| dc.type | text |