How rare are diffusive rare events?

Details How rare are diffusive rare events? How rare are diffusive rare events?

2008-04-08

arxiv.org/abs/0804.1165v1

Europhys. Lett. 82(4), 40005 (2008)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 5 figures. Accepted for publication in Europhysics Letters (http://www.iop.org/EJ/journal/EPL)

Scientific paper

10.1209/0295-5075/82/40005

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.

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