The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …

In this study we derive a single-particle equation of motion, from first principles, starting out
with a microscopic description of a tracer particle in a one-dimensional many-particle system …

We investigate the full functional form of the first passage time density (FPTD) of a tracer
particle in a single-file diffusion (SFD) system whose population is:(i) homogeneous, ie, all …

We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file
dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Δ …

We study the diffusion of tagged hard-core interacting Brownian point particles under the
influence of an external force field in one dimension. Using the Jepsen line we map this …

We consider the symmetric exclusion particle system on Z starting from an infinite particle
step configuration in which there are no particles to the right of a maximal one. We show that …

We investigate the single-file dynamics of a tagged particle in a system consisting of N
hardcore interacting particles (the particles cannot pass each other) which are diffusing in a …

This thesis both broadens and deepens our understanding of the Brownian world. It
addresses new problems in diffusion theory that have recently attracted considerable …

We address the question of the time needed by N particles, initially located on the first sites
of a finite one-dimensional lattice of size L, to exit that lattice when they move according to a …

We compute the full probability distribution of the positions of a tagged particle exactly for the
given arbitrary initial positions of the particles, and for general single-particle propagators …