Related papers: Localization of directed polymers with general ref…
We consider homogeneous open quantum random walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position…
We study the geometry of a semiflexible polymer at finite temperatures. The writhe can be calculated from the properties of Gaussian random walks on the sphere. We calculate static and dynamic writhe correlation functions. The writhe of a…
We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers $\pm q_0$. Such polymers, known as polyampholytes, are compact when completely neutral and expanded when highly charged. Our…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
We study the question of how the competition between $\textit{bulk disorder}$ and a $\textit{localized microscopic defect}$ affects the macroscopic behavior of a system in the directed polymer context at the free energy level. We consider…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is used to study polymer growth near a $D$-dimensional attractive hyperspherical boundary. The…
Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…
We consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^d. The parameters of the distribution are a 2d-uplet of…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting…
Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of…
For a long time one has associated to the Quantum Heisenberg Ferromagnet on a lattice, a random walk on the permutation group of the lattice vertices. We here present a polymer expansion for the solution of the heat equation coupled to the…
We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…
Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk…
We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature…
In this chapter we review the rich behavior of polymer chains embedded in a quenched random environment. We first consider the problem of a Gaussian chain free to move in a random potential with short-ranged correlations. We derive the…
We apply the Dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape. We study the geometrical and energetic scaling properties of the optimal path where the energies are…
Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover…
We provide a new short and elementary proof of diffusivity for directed polymer in a random environment in the weak disorder phase.
The distribution of monomers in a coating of grafted and adsorbing polymers is modelled using a grafted staircase polygon in the square lattice. The adsorbing staircase polygon consists of a bottom and a top lattice path (branches) and the…