Algebraic Probability Theory

A large part of probability theory is the study of operations on, and convergence of, probability distributions. The most frequently used operations turn the set of distributions into a semigroup. A considerable part of probability theory can be expressed, proved, sometimes even understood in terms of the abstract theory of topological semigroups. The authors 'algebraic probability theory' is a field where problems stem mainly from probability theory, have an arithmetical flair and are often dressed in terms of algebra, while the tools employed frequently belong to the theory of (complex) functions and abstract harmonic analysis. It lies at the cross-roads of numerous mathematical theories, and should serve as a catalyst to further research.