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We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via…
We study the directed polymer (DP) of length $t$ in a random potential in dimension 1+1 in the continuum limit, with one end fixed and one end free. This maps onto the Kardar-Parisi-Zhang growth equation in time $t$, with flat initial…
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 calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the n-th moment <Z^n> of the partition function is given by the ground state energy…
This thesis deals with some $(1+1)$-dimensional lattice path models from the KPZ universality class: the directed random polymer with inverse-gamma weights (known as log-gamma polymer) and its zero temperature degeneration, i.e. the last…
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 the solution of the stochastic heat equation \partial_T \mathcal{Z} = 1/2 \partial_X^2 \mathcal{Z} - \mathcal{Z} \dot{\mathscr{W}} with delta function initial condition \mathcal{Z} (T=0)= \delta_0 whose logarithm, with…
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 consider the limit behavior of partition function of directed polymers in random environment represented by linear model instead of a family of i.i.d.variables in $1+1$ dimensions. Under the assumption that the correlation decays…
We study a one dimensional directed polymer model in an inverse-gamma random environment, known as the log-gamma polymer, in three different geometries: point-to-line, point-to-half line and when the polymer is restricted to a half space…
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…
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…
We consider two directed polymer models in the Kardar-Parisi-Zhang (KPZ) universality class: the O'Connell-Yor semi-discrete directed polymer with boundary sources and the continuum directed random polymer with (m,n)-spiked boundary…
The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…
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…
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…
In this paper, we consider four integrable models of directed polymers for which the free energy is known to exhibit KPZ fluctuations. A common framework for the analysis of these models was introduced in our recent work on the…
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…
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…
We consider the convergence of partition functions and endpoint density for the half-space directed polymer model in dimension $1+1$ in the intermediate disorder regime as considered for the full space model by Alberts, Khanin and Quastel…