Related papers: Weak disorder for low dimensional polymers: The mo…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…
We study one-dimensional nearest neighbour random walk in site-random environment. We establish precise (sharp) large deviations in the so-called ballistic regime, when the random walk drifts to the right with linear speed. In the…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
We show that the weak disorder phase for the directed polymer model in a bounded random environment is characterized by the integrability of the running supremum $\sup_{n\in \mathbb N}W_n^\beta$ of the associated martingale…
The one dimensional direct polymer in random media model is investigated using a variational approach in the replica space. We demonstrate numerically that the stable point is a maximum and the corresponding statistical properties for the…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
We study the quenched behaviour of a perturbed version of the simple symmetric random walk on the set of integers. The random walker moves symmetrically with an exception of some randomly chosen sites where we impose a random drift. We show…
A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of $d\times d$ inverse-Wishart random matrices, so that the model nicely generalizes the well-studied log-gamma…
We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…
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…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
The a.s. existence of a polymer probability in the infinite volume limit is readily obtained under general conditions of weak disorder from standard theory on multiplicative cascades or branching random walk. However, speculations in the…
A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The…
In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong…
In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not…
A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by…