Related papers: Random walk models and probabilistic techniques fo…
Based on the analogy with the quantum mechanics of a particle propagating in a {\em complex} potential, we develop a field-theoretical description of the statistical properties of a self-avoiding polymer chain in a random environment. We…
The phase structure of a homopolymer chain is investigated in terms of a universal theoretical model, designed to describe the infrared limit of slow spatial variations. The effects of chirality are studied and compared with the influence…
Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…
We study self avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well…
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…
We study the conformation and dynamics of a single polymer chain that is pulled by a constant force applied at its one end with the other end free. Such a situation is relevant to the growing technology of manipulating individual…
In this article we study a \emph{non-directed} polymer model in dimension $d\ge 2$: we consider a simple symmetric random walk on $\mathbb{Z}^d$ which interacts with a random environment, represented by i.i.d. random variables…
We consider a class of inhomogeneous media known as composite media that is often encountered in experimental sciences and investigate the persistence probability of a random walker in such a system. Analytical and numerical results for the…
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
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 a one-dimensional continuous time random walk with transition rates depending on an underlying autonomous simple symmetric exclusion process starting out of equilibrium. This model represents an example of a random walk in a…
In this article we study a one dimensional model for a polymer in a poor solvent: the random walk on $\mathbb{Z}$ penalized by its range. More precisely, we consider a Gibbs transformation of the law of the simple symmmetric random walk by…
We consider a directed random walk model of a random heterogeneous polymer in the proximity of an interface separating two selective solvents. This model exhibits a localization/delocalization transition. A positive value of the free energy…
Dimerization and subsequent aggregation of polymers and biopolymers often occur under nonequilibrium conditions. When the initial state of the polymer is not collapsed or the final folded native state, the dynamics of dimerization can…
We construct a new statistical physical model of polymer translocation through a pore in a membrane treated as the diffusion process across a free energy barrier. We determine the translocation time in terms of chain flexibility yielding an…
Polymers with active segments constitute prospective future materials and are used as a model for some biological systems such as chromatin. The directions of the active forces are typically introduced with temporal or spatial correlations…
We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs…
We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…