Related papers: Continuous Markovian model for Levy random walks w…
Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous…
The emergence of heavy-tailed statistics in complex systems is conventionally attributed to non-local stochastic jumps or non-Markovian memory. Here, we present a one-dimensional random walk where power-law behaviors arise instead from a…
L\'evy flights and L\'evy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities are discontinuity versus continuity of their trajectories and…
The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This…
We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker,…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…
Search strategies based on random walk processes with long-tailed jump length distributions (Levy walks) on the one hand and intermittent behavior switching between local search and ballistic relocation phases on the other, have been…
We introduce a model for translational molecular motors to demonstrate that a multivalent catalytic walker with flexible, uncoordinated legs can transform the free energy of surface-bound substrate sites into mechanical work and undergo…
We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…
Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts…
The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is…
We study a two-dimensional diffusive motion of a tracer particle in restricted, crowded anisotropic geometries. The underlying medium is the same as in our previous work [J. Chem. Phys. 140, 044706 (2014)] in which standard, gaussian…
This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply.…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin…
In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and…
We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of…
Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism…