|Dept.||University of Kaiserslautern|
Abstract: The theory of interacting particle systems enables a rigorous analysis of several models that arise in statistical mechanics, biology, economy and other fields. We give an introduction to the theory of interacting particle systems. Our approach is based on the geometry and analysis on continuous configuration space in dimension d. As application we study a contact model in continuum, which describes the spread of an infectious disease. Technically, the contact process is a Markov process on a space of spin configurations. From the evolution of large, interacting particles systems (microscopic models) one can derive mean-field evolution equations. This aspect will also be discussed.