The survival probability of a branching random walk in presence of an absorbing wall
| dc.creator | Derrida, B. | |
| dc.creator | Simon, D. | |
| dc.date | 2007-03-13 | |
| dc.date | 2007-07-23 | |
| dc.date.accessioned | 2026-07-07T08:19:28Z | |
| dc.date.available | 2026-07-07T08:19:28Z | |
| dc.description | A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as v varies. The problem can be analyzed using the properties of the Fisher-Kolmogorov-Petrovsky-Piscounov (F-KPP) equation. We find that the survival probability of the branching random walk vanishes at a critical velocity v_c of the wall with an essential singularity and we characterize the divergences of the relaxation times for v<v_c and v>v_c. At v=v_c the survival probability decays like a stretched exponential. Using the F-KPP equation, one can also calculate the distribution of the population size at time t conditionned by the survival of one individual at a later time T>t. Our numerical results indicate that the size of the population diverges like the exponential of (v_c-v)^{-1/2} in the quasi-stationary regime below v_c. Moreover for v>v_c, our data indicate that there is no quasi-stationary regime. | |
| dc.description | References and one figure added | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0703353 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0703353 | |
| dc.identifier | EPL, 78 (2007) 60006 | |
| dc.identifier | doi:10.1209/0295-5075/78/60006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134774 | |
| dc.subject | Statistical Mechanics | |
| dc.title | The survival probability of a branching random walk in presence of an absorbing wall | |
| dc.type | text |