Ergodic theory and hydrodynamic limit for run-and-tumble particle processes

In this thesis we will study the ergodic measures and the hydrodynamic limit of independent run-and-tumble particle processes, i.e., an interacting particle system for particles with an internal energy source, which makes them move in a preferred direction that changes at random times. We start by providing some basic concepts and theory of...

The Blum-Hanson Property

The Blum-Hanson property was identified in the 1960's as a property closely related to that of strong mixing. This property is interesting in the field of ergodic theory. It can be shown that if the orbits of all points have the Blum-Hanson property, then the operator is strongly mixing. The converse is not always true and much research has been...