  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 $\{k_i(t)\}\equiv[k_1(t),k_2(t),...,k_{N(t)}(t)]$ of the
constituent particles, where $N(t)$ is the total number of particles in that
realization at time $t$. When $\{k_i(t)\}$ 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
$k_f(t)=\text{max}[k_1(t),k_2(t),...,k_{N(t)}(t)]$. Due to interparticle
interactions, $\{k_i(t)\}$ at two different times for a single front
realization are naturally not independent of each other, and thus the
probability distribution $P_{k_f}(t)$ [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, $P_{k_f}(t)$ is Gaussian. In a bosonic front model
however, we observe small deviations from the Gaussian.
