Random walk is a fundamental concept with applications ranging from quantum physics to
econometrics. Remarkably, one specific model of random walks appears to be ubiquitous …

In this article we demonstrate the very inspiring role of the continuous-time random walk
(CTRW) formalism, the numerous modifications permitted by its flexibility, its various …

We show the relation between processes which are modeled by a Langevin equation with
multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent …

The big-jump principle is a well-established mathematical result for sums of independent
and identically distributed random variables extracted from a fat-tailed distribution. It states …

Lévy flights and Lévy walks serve as two paradigms of random walks resembling common
features but also bearing fundamental differences. One of the main dissimilarities is the …

Let us now consider the Fokker-Planck equation, which is a partial differential equation that
describes the time evolution of the PDF of the positions of particles, and was introduced in …

We review some extensions of the continuous time random walk first introduced by Elliott
Montroll and George Weiss more than 50 years ago [EW Montroll, GH Weiss, J. Math. Phys …

We study a particle immersed in a heat bath, in the presence of an external force which
decays at least as rapidly as 1/x, eg, a particle interacting with a surface through a Lennard …

We investigate a basic model of nonlinear Brownian motion in a thermal environment, where
nonlinear friction interpolates between viscous Stokes and dry Coulomb friction. We show …

We address the problem of telegraphic transport in several dimensions. We review the
derivation of two and three dimensional telegrapher's equations—as well as their fractional …