Motion of particles in many systems exhibits a mixture between periods of random diffusive-
like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous …

We consider a generalization of a one-dimensional stochastic process known in the physical
literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line …

We consider a persistent random walk on an inhomogeneous environment where the
reflection probability depends only on the distance from the origin. Such an environment is …

We consider a continuous-time random walk which is defined as an interpolation of a
random walk on a point process on the real line. The distances between neighboring points …

It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic
theory is trivial; it states that for any infinite-measure-preserving ergodic system, the Birkhoff …

In this letter we consider the phase diffusion of a harmonically driven undamped pendulum
and show that it is anomalous in the strong sense. The role played by the fractal properties …

Many physical and biological processes are modeled by “particles" undergoing Lévy
random walks. A feature of significant interest in these systems is the mean square …

The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport
emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers …

We study a random walk on a point process given by an ordered array of points (ω k, k∈ Z)
on the real line. The distances ω k+ 1− ω k are iid random variables in the domain of …

This dissertation details our research on random walks seen as simple mathematical models
useful to describe the complex dynamics of many physical systems. In particular, we focus …