Quasi-stationary regime of a branching random walk in presence of an absorbing wall
| dc.creator | Simon, Damien | |
| dc.creator | Derrida, Bernard | |
| dc.date | 2007-10-19 | |
| dc.date | 2008-02-12 | |
| dc.date.accessioned | 2026-07-07T09:19:43Z | |
| dc.date.available | 2026-07-07T09:19:43Z | |
| dc.description | A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time $T$. We study the quasi-stationary regime for $v<v_c$ when $T$ is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time $T$. We then use this construction to show that the properties of the quasi-stationary regime are universal when $v\to v_c$. We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map. | |
| dc.description | 2 figures, minor corrections, one reference added | |
| dc.identifier | https://arxiv.org/abs/0710.3689 | |
| dc.identifier | http://arxiv.org/abs/0710.3689 | |
| dc.identifier | doi:10.1007/s10955-008-9504-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154494 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Populations and Evolution | |
| dc.title | Quasi-stationary regime of a branching random walk in presence of an absorbing wall | |
| dc.type | text |