2012/09/19 by David Applebaum, Applebaum, David, A. H. Dooley +2
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Random Matrices and Applications #advanced mathematical theories #math.PR
paper · pdf · doi:10.48550/arxiv.1209.4217
openalex publication_date 2012/09/19 · arxiv created 2013/05/21 · arxiv updated 2013/05/22 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In 1964 R.Gangolli published a Lévy-Khintchine type formula which characterised K bi-invariant infinitely divisible probability measures on a symmetric space G/K. His main tool was Harish-Chandra's spherical functions which he used to construct a generalisation of the Fourier transform of a measure. In this paper we use generalised spherical functions (or Eisenstein integrals) and extensions of these which we construct using representation theory to obtain such a characterisation for arbitrary infinitely divisible probability measures on a non-compact symmetric space. We consider the example of hyperbolic space in some detail.