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

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.

17 pages, 2 figures, the final version, two paragraphs added to the conclusion

References in corpus (3)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Optimal fluctuation approach to a directed polymer in a random medium
• Joint free energy distribution in the random directed polymer problem

Cited by in corpus (18)

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• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• Inverse scattering solution of the weak noise theory of the Kardar-Parisi-Zhang equation with flat and Brownian initial conditions
• The crossover from the Macroscopic Fluctuation Theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion
• Height distribution tails in the Kardar-Parisi-Zhang equation with Brownian initial conditions
• Observing symmetry-broken optimal paths of stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media
• Large fluctuations of a Kardar-Parisi-Zhang interface on a half-line: the height statistics at a shifted point
• Time-averaged height distribution of the Kardar-Parisi-Zhang interface
• Local average height distribution of fluctuating interfaces
• Integrability in the weak noise theory
• Scaling at the OTOC Wavefront: free versus chaotic models
• Short-time large deviations of the spatially averaged height of a KPZ interface on a ring
• Exact short-time height distribution and dynamical phase transition in the relaxation of a Kardar-Parisi-Zhang interface with random initial condition
• Large deviations of the interface height in the Golubović-Bruinsma model of stochastic growth
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• Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas