Construction of classical and quantum gases

A point process is a mechanism which realizes at random locally finite particle configurations in space. One of the main results of the present work is the construction of a class of point processes which extends considerably the class of infinitely divisible processes. This is done by means of a combination of classical methods from the theory of random measures and the method of cluster expansions from statistical mechanics. A representation theorem for the factorial measures of such processes is given which allows to identify permanental and determinantal processes. The new method then allows, in combination with the recently developed cluster estimates of Poghosyan and Ültschi, the construction of infinitely extented Gibbs, Bose and polymer processes. This work then terminates with the study of thinning and splitting of processes. For instance, by means of the thinning operation a certain class of these processes is identified as doubly stochastic Poisson processes.