This comprehensive monograph covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and serves both as an introductory text and as a reference for the expert.Expand

It is shown that for a large class of interactions any canonical Gibbs state satisfying a natural temperedness condition is a mixture of Gibbs states with appropriate activities, and vice versa. Some… Expand

We establish phase transitions for a class of continuum multi-type particle systems with finite range repulsive pair interaction between particles of different type. This proves an old conjecture of… Expand

AbstractThe Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and… Expand

SummaryWe establish large deviation principles for the stationary and the individual empirical fields of Poisson, and certain interacting, random fields of marked point particles in ℝd. The… Expand

SummaryFor Gibbsian systems of particles inRd, we investigate large deviations of the translation invariant empirical fields in increasing boxes. The particle interaction is given by a superstable,… Expand

We establish the existence of stationary Gibbsian point processes for interactions that act on hyperedges between the points. For example, such interactions can depend on Delaunay edges or triangles,… Expand

For supercritical multitype Markov branching processes in continuous time, the evolution of types along those lineages that survive up to some time t is investigated, and almost-sure convergence theorems for both time and population averages of ancestral types are established.Expand