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The free-energy distribution function of an elastic string in a quenchedrandom potential, P(F), is investigated with the help of theoptimal-fluctuation approach. The form of the far-right tail of P(F) is foundby constructing the exact solution of the non-linear saddle-point equationsdescribing the asymptotic form of the optimal fluctuation. The solution of theproblem is obtained for two different types of boundary conditions and for anarbitrary dimension of the imbeding space 1+d with d from the interval 0<d<2.The results are also applicable for the description of the far-left tail of theheight distribution function in the stochastic growth problem described by thed-dimensional Kardar-Parisi-Zhang equation.

Explicit solution of the optimal fluctuation problem for an elastic string in random potential