Abstract
The optimal-fluctuation approach is applied to study the most distant (nonuniversal) tails of the free-energy distribution function ${P}_{L}(F)$ for an elastic string (of a large but finite length $L$) interacting with a quenched random potential. A further modification of this approach is proposed which takes into account the renormalization effects and allows one to study the closest (universal) parts of the tails. The problem is analyzed for different dimensions of a space in which the polymer is imbedded. In terms of the stochastic growth problem, the same distribution function describes the distribution of heights in the regime of a nonstationary growth in the situation when an interface starts to grow from a flat configuration.
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