2004/01/31 by Debabrata Panja
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.soft
paper · pdf · doi:10.1103/physreve.70.036101
published as Phys. Rev. E 70, 036101 (2004) · 6 pages, 3 figures, miniscule changes on the previous version, to appear in Phys. Rev. E
arxiv created 2004/05/09 · arxiv updated 2009/12/01
In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time t by the set of co-ordinates \ki(t)\≡[k1(t),k2(t),...,kN(t)(t)] of the constituent particles, where N(t) is the total number of particles in that realization at time t. When \ki(t)\ are arranged in the ascending order of magnitudes, the instantaneous front position can be denoted by the location of the rightmost particle, i.e., by the extremal value kf(t)=max[k1(t),k2(t),...,kN(t)(t)]. Due to interparticle interactions, \ki(t)\ at two different times for a single front realization are naturally not independent of each other, and thus the probability distribution Pkf(t) [based on an ensemble of such front realizations] describes extreme value statistics for a set of correlated random variables. In view of the fact that exact results for correlated extreme value statistics are rather rare, here we show that for a fermionic front model in a reaction-diffusion system, Pkf(t) is Gaussian. In a bosonic front model however, we observe small deviations from the Gaussian.