Related papers: Exactly Solvable Model of Random Walks with Stocha…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
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…
A system of interacting walkers is considered in a two-dimensional hypothetical space, where the dynamics of each walker are governed by the opinion states of the agents of a fully connected three-state opinion dynamics model. Such walks,…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, Poisson-distributed, tumble duration so that a…
The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial differential equations) of such processes are well established,…
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…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We analyze a model for a walker moving on a ratchet potential. This model is motivated by the properties of transport of motor proteins, like kinesin and myosin. The walker consists of two feet represented as two particles coupled…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
We study dynamic random conductance models on $\mathbb{Z}^2$ in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally…
We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions…
The time-dependent work probability distribution function $P(W)$ is investigated analytically for a diffusing particle trapped by an anisotropic harmonic potential and driven by a nonconservative drift force in two dimensions. We find that…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…