Related papers: Random walk models and probabilistic techniques fo…
We analyze a (1+1)-dimension directed random walk model of a polymer dipped in a medium constituted by two immiscible solvents separated by a flat interface. The polymer chain is heterogeneous in the sense that a single monomer may…
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
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 self-avoid random walk algorithm has been extensively used in the study of polymers. In this work we study the basic properties of the trajectories generated with this algorithm when two interactions are added to it: contact and folding…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
In this article, I study the localization transition of an hydrophobic homopolymer in interaction with an interface between oil and water. To that aim I consider a model in which the trajectories of a simple random walk play the role of the…
We consider a general model of a heterogeneous polymer chain fluctuating in the proximity of an interface between two selective solvents. The heterogeneous character of the model comes from the fact that the monomer units interact with the…
These lecture notes are a guided tour through the fascinating world of polymer chains interacting with themselves and/or with their environment. The focus is on the mathematical description of a number of physical and chemical phenomena,…
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…
This paper studies a polymer chain in the vicinity of a linear interface separating two immiscible solvents. The polymer consists of random monomer types, while the interface carries random charges. Both the monomer types and the charges…
We study the conformational properties of heteropolymers containing two types of monomers A and B, modeled as self-avoiding random walks on a regular lattice. Such a model can describe in particular the sequences of hydrophobic and…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…
In this article we study a \emph{non-directed polymer model} on $\mathbb Z$, that is a one-dimensional simple random walk placed in a random environment. More precisely, the law of the random walk is modified by the exponential of the sum…
In this work we derive certain topological theories of transverse vector fields whose amplitudes reproduce topological invariants involving the interactions among the trajectories of three and four random walks. This result is applied to…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on…
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…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…