Related papers: Random walk models and probabilistic techniques fo…
Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…
We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.
Molecular process of polymer collapse was reproduced by isothermal molecular dynamics simulation. The initial polymer chains were obtained by mean of random walks in continuum space. Two potential models were considered to represent short…
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…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
Molecular dynamics simulation methods are used to study the folding of polymer chains into packed cubic states. The polymer model, based on a chain of linked sites moving in the continuum, includes both excluded volume and torsional…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long confined flexible polymer chain; and the confinement condition is achieved by two parallel athermal plates. The…
We consider d-dimensional random surface models which for d=1 are the standard (tied-down) random walks (considered as a random ``string''). In higher dimensions, the one-dimensional (discrete) time parameter of the random walk is replaced…
Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its…
We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in 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…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
The aim of this paper is to investigate the distribution of a continuous polymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously and independently vary two…
The aim of this paper is to investigate the distribution of a continuous homopolymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously vary two parameters: the…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical…