Lévy processes in free probability

  1. Ole E. Barndorff-Nielsen† and
  2. Steen Thorbjørnsen‡,§
  1. †Department of Mathematical Sciences, University of Aarhus, DK-8000 Aarhus C, Denmark; and ‡Department of Mathematics and Computer Science, University of Southern Denmark, 5230 Odense M, Denmark

  1. Edited by Richard V. Kadison, University of Pennsylvania, Philadelphia, PA, and approved October 7, 2002 (received for review January 29, 2002)

Abstract

This is the continuation of a previous article that studied the relationship between the classes of infinitely divisible probability measures in classical and free probability, respectively, via the Bercovici–Pata bijection. Drawing on the results of the preceding article, the present paper outlines recent developments in the theory of Lévy processes in free probability.

Footnotes

  • ↵ § To whom correspondence should be addressed. E-mail: steenth{at}imada.sdu.dk.

  • This paper was submitted directly (Track II) to the PNAS office.

  • ↵ Compare with 3.3 Remark below.

  • Abbreviations:

    1. w.r.t., with respect to

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  1. Published online before print December 9, 2002, doi: 10.1073/pnas.232598299 PNAS December 24, 2002 vol. 99 no. 26 16576-16580
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