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

TL;DR

This paper investigates the extreme tails of the free-energy distribution in directed polymers and KPZ growth, distinguishing between universal and non-universal behaviors through an advanced fluctuation approach.

Contribution

It introduces a modified optimal fluctuation method that accounts for renormalization effects, enabling analysis of both universal and non-universal distribution tails across different dimensions.

Findings

Characterization of non-universal tail behaviors in free-energy distributions.

Identification of universal tail regimes in the KPZ height distribution.

Application of the approach to various spatial dimensions.

Abstract

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.