Related papers: Universality for directed polymers in thin rectang…
Polymer's network is treated as an anisotropic fractal with fractional dimensionality D = 1 + \epsilon close to one. Percolation model on such a fractal is studied. Using the real space renormalization group approach of Migdal and Kadanoff…
We study the $1+1$-dimensional random directed polymer problem, i.e., an elastic string $\phi(x)$ subject to a Gaussian random potential $V(\phi,x)$ and confined within a plane. We mainly concentrate on the short-scale and…
It is demonstrated on a realistic model of amorphous alloy Si$_{0.9}$Ge$_{0.1}$ with 1000 atoms, that short-range spectral fluctuations of propagons and diffusons are universal and in agreement with random matrix theory. The universality…
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…
We consider the low-temperature $T<T_c$ disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$) and 1+3 (where $T_c<\infty$). To characterize the localization properties of the polymer of…
The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the…
The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel~\cite{AKQ12}. It was proved that at inverse temperature $\beta n^{-\gamma}$ with $\gamma=1/4$ the partition function, centered…
We find numerically that the sample to sample fluctuation of the entropy, $\Delta S$, is a tool more sensitive in distinguishing how from high temperature behaviors, than the corresponding fluctuation in the free energy. In 1+1 dimensions…
In this short note, we prove a central limit theorem for a type of replica overlap of the Brownian directed polymer in a Gaussian random environment, in the low temperature regime and in all dimensions. The proof relies on a…
Directed polymers in random environment have usually been constructed with a simple random walk on the integer lattice. It has been observed before that several standard results for this model continue to hold for a more general reference…
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…
We prove that in the full $L^2$-regime the partition function of the directed polymer model in dimensions $d\geq 3$, if centered, scaled and averaged with respect to a test function $\varphi \in C_c(\mathbb{R}^d)$, converges in distribution…
We propose an Ansatz for Universal conductance fluctuations in continuous dimensions from 0 up to 4. The Ansatz agrees with known formulas for integer dimensions 1, 2 and 3, both for hard wall and periodic boundary conditions. The method is…
In a conducting medium held at finite temperature, free carriers are performing Brownian motion and generate fluctuating electromagnetic fields. We compute the averaged Lorentz force density that turns out nonzero in a thin sub-surface…
We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the…
We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and…
The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
We prove that the random variable $\ct=\argmax_{t\in\rr}\{\aip(t)-t^2\}$ has tails which decay like $e^{-ct^3}$. The distribution of $\ct$ is a universal distribution which governs the rescaled endpoint of directed polymers in 1+1…