How rare are diffusive rare events?
| dc.creator | Sanders, David P. | |
| dc.creator | Larralde, Hernán | |
| dc.date | 2008-04-08 | |
| dc.date.accessioned | 2026-07-07T09:38:58Z | |
| dc.date.available | 2026-07-07T09:38:58Z | |
| dc.description | We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlations makes this problem analytically intractable. However, for a mean-field approximation in which the walkers can jump anywhere in the system, we obtain a simple asymptotic form for the mean first-passage time to have a given number k of particles at a distinguished site. We show numerically, and argue heuristically, that for large enough k, the mean-field results give a good approximation for first-passage times for systems with nearest-neighbour dynamics, especially for two and higher spatial dimensions. Finally, we show how the results change when density fluctuations anywhere in the system, rather than at a specific distinguished site, are considered. | |
| dc.description | 6 pages, 5 figures. Accepted for publication in Europhysics Letters (http://www.iop.org/EJ/journal/EPL) | |
| dc.identifier | https://arxiv.org/abs/0804.1165 | |
| dc.identifier | http://arxiv.org/abs/0804.1165 | |
| dc.identifier | Europhys. Lett. 82(4), 40005 (2008) | |
| dc.identifier | doi:10.1209/0295-5075/82/40005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161006 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | How rare are diffusive rare events? | |
| dc.type | text |