Volume 82, Number 4, May 2008
|Number of page(s)||6|
|Published online||14 May 2008|
How rare are diffusive rare events?
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México - Apartado Postal 48-3, 62551 Cuernavaca, Morelos, Mexico
Corresponding author: email@example.com
Accepted: 5 April 2008
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.40.Fb – Random walks and Levy flights / 05.60.-k – Transport processes
© EPLA, 2008
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