Optimal fluctuation approach to a directed polymer in a random medium

Abstract

A modification of the optimal fluctuation approach is applied to study the tails of the free energy distribution function P(F) for an elastic string in quenched disorder both in the regions of the universal behavior of P(F) and in the regions of large fluctuations, where the behavior of P(F) is non-universal. The difference between the two regimes is shown to consist in whether it is necessary or not to take into account the renormalization of parameters by the fluctuations of disorder in the vicinity of the optimal fluctuation.