Universal and non-universal tails of distribution functions in the directed polymer and KPZ problems

Understand

The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(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 most close (universal) parts of the tails.
• The problem is analyzed for different dimensions of a space in which the polymer is imbedded.
• In terms the stochastic growth problem, the same distribution function describes the distribution of heights in the regime of a non-stationary growth in a situation when an interface starts to grow from a flat configuration.