Related papers: Conservative random walks in confining potentials
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…
We study whether a multivariate L\'evy-driven moving average process can shadow arbitrarily closely any continuous path, starting from the present value of the process, with positive conditional probability, which we call the conditional…
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties.…
We consider two continuous-time generalizations of conservative random walks introduced in [J.Englander and S.Volkov (2022)], an orthogonal and a spherically-symmetrical one; the latter model is known as {\em random flights}. For both…
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process…
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…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
The L\'evy flight foraging hypothesis states that organisms must have evolved adaptations to exploit L\'evy walk search strategies. Indeed, it is widely accepted that inverse square L\'evy walks optimize the search efficiency in foraging…
We present theoretical and experimental results of L\'evy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…
Spatial spread of minority carriers produced by optical excitation in semiconductors is usually well described by a diffusion equation. The classical diffusion process can be viewed as a result of a random walk of particles in which every…
The integro-differential wave equation for the probability density function for a classical one-dimensional L\'evy walk with continuous sample paths has been derived. This equation involves a classical wave operator together with memory…
Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically…
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…
The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…
We study the transmission of random walkers through a finite-size inhomogeneous material with a quenched, long-range correlated distribution of scatterers. We focus on a finite one-dimensional structure where walkers undergo random…
Standard Reaction-Diffusion (RD) systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle…
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…