title: Lévy laws in free probability.
abstract: This article and its sequel outline recent developments in the theory of infinite divisibility and Lévy processes in free probability, a subject area belonging to noncommutative (or quantum) probability. The present paper discusses the classes of infinitely divisible probability measures in classical and free probability, respectively, via a study of the Bercovici-Pata bijection between these classes.
authors.affiliation: Department of Mathematical Sciences, University of Aarhus, DK-8000 Aarhus C, Denmark.
authors.forename: Ole E
authors.initials: OE
authors.lastname: Barndorff-Nielsen
authors.forename: Steen
authors.initials: S
authors.lastname: Thorbjørnsen