Related papers: The discrete-time parabolic Anderson model with he…
We investigate a celebrated problem of one dimensional tight binding model in the presence of disorder leading to Anderson localization from a novel perspective. A binary disorder is assumed to be created by immobile heavy particles for the…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We derive exact asymptotics of time correlation functions for the parabolic Anderson model with homogeneous initial condition and time-independent tails that decay more slowly than those of a double exponential distribution and have a…
We analyze, via Imry-Ma scaling arguments, the strong disorder phases that exist in low dimensions at all temperatures for directed polymers and interfaces in random media. For the uncorrelated Gaussian disorder, we obtain that the optimal…
We study the adsorption-desorption phase transition of directed branched polymer in $d+1$ dimensions in contact with a line by mapping it to a $d$ dimensional hard core lattice gas at negative activity. We solve the model exactly in 1+1…
We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion…
Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This…
We consider a continuous one dimensional model of two charged interacting particles in a random potential. The electric repulsion is strictly one dimensional and it inhibits Anderson localization. In fact, the spectrum is continuous. The…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at…
We show that in the one-dimensional (1D) Anderson model long-range correlations within the sequence of on-site potentials may lead to a region of extended states in the vicinity of the band centre, i.e., to a correlation-induced…
We consider the solution to the parabolic Anderson model with homogeneous initial condition in large time-dependent boxes. We derive stable limit theorems, ranging over all possible scaling parameters, for the rescaled sum over the solution…
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling…
The competition in the pinning of a directed polymer by a columnar pin and a background of random point impurities is investigated systematically using the renormalization group method. With the aid of the mapping to the noisy-Burgers'…
We give a new expression for the law of the eigenvalues of the discrete Anderson model on the finite interval $[0,N]$, in terms of two random processes starting at both ends of the interval. Using this formula, we deduce that the tail of…
We consider the Anderson model at large disorder on $\mathbb{Z}^2$ where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These…
The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically and numerically that extended states may occur in the one- and…
Dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations…
We consider the parabolic Anderson model, the Cauchy problem for the heat equation with random potential in $Z^d$. We use i.i.d. potentials $\xi: Z^d \to \R$ in the third universality class, namely the class of almost bounded potentials, in…
In this paper, we consider directed polymers in random environment with long range jumps in discrete space and time. We extend to this case some techniques, results and classifications known in the usual short range case. However, some…