Related papers: Two-point free energy distribution function in (1+…
Explicit expression for the $N$-point free energy distribution function in one dimensional directed polymers in a random potential is derived in terms of the Bethe ansatz replica technique. The obtained result is equivalent to the one…
The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the…
The explicit expression for the two time free energy distribution function in one-dimensional random directed polymers is derived in terms of the Bethe ansatz replica technique. It is show that such type of the distribution function can be…
The asymptotic analytic expression for the two-time free energy distribution function in (1+1) random directed polymers is derived in the limit when the two times are close to each other
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…
The explicit expression for the the probability distribution function of the endpoint fluctuations of one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated…
We study the statistical properties of one-dimensional directed polymers in a short-range random potential by mapping the replicated problem to a many body quantum boson system with attractive interactions. We find the full set of…
We consider a 1+1 dimensional directed continuum polymer in a Gaussian delta-correlated space-time random potential. For this model the moments (= replica) of the partition function, Z(x,t), can be expressed in terms of the attractive…
We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is…
We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in presence of disorder, equivalent to the KPZ equation on the half space with droplet initial conditions. From a Bethe Ansatz solution of the…
The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions.…
The joint statistical properties of two free energies computed at two different temperatures in {\it the same sample} of $(1+1)$ directed polymers is studied in terms of the replica technique. The scaling dependence of the reduced free…
We give sharp estimate for the free energy of directed polymers in random environment in dimension 1+1. This estimate was known for a Gaussian environment, we extend it to the case where the law of the environment is infinitely divisible.
The discrete polymer model with random Boltzmann weights with homogeneous inverse gamma distribution, introduced by Sepp\"al\"ainen, is studied in the case of a polymer with one fixed and one free end. The model with two fixed ends has been…
We consider two configurations of a random directed polymer of length L confined to a plane and ending in two points separated by 2u. Defining the mean free energy $\bar F$ and the free energy difference F' of the two configurations, we…
We study the partition function of two versions of the continuum directed polymer in 1+1 dimension. In the full-space version, the polymer starts at the origin and is free to move transversally in the reals, and in the half-space version,…
We prove a formula conjectured in O'Connell and Yor (2001) for the free energy density of a directed polymer in a Brownian environment in 1+1 dimensions.
The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive…
The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to the $N$-particle quantum boson system with attractive…
In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which allows to compute the scaling exponent $\theta$ of the free energy…