Lévy laws in free probability.

  title={L{\'e}vy laws in free probability.},
  author={Ole E. Barndorff-Nielsen and Steen Thorbj\ornsen},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  volume={99 26},
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.