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Topics in Probability and Lie Groups: Boundary Theory
Edited by: J. C. Taylor, McGill University, Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Proceedings & Lecture Notes
2001; 202 pp; softcover
Volume: 28
ISBN-10: 0-8218-0275-5
ISBN-13: 978-0-8218-0275-5
List Price: US$72
Member Price: US$57.60
Order Code: CRMP/28
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This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figà-Talomanaca. These articles arose from a Centre de Recherches de Mathématiques (CRM) seminar entitiled, "Topics in Probability on Lie Groups: Boundary Theory".

Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on \(d\) generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figà-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space.

The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.

Titles in this series are co-published with the Centre de Recherches Mathématiques.


Graduate students and research mathematicians interested in probability theory and stochastic processes.

Table of Contents

  • J.-P. Anker and L. Ji -- Heat kernel and Green function estimates on noncompact symmetric spaces. II
  • S. N. Evans -- Local fields, Gaussian measures, and Brownian motions
  • A. Figà-Talamanca -- An application of Gelfand pairs to a problem of diffusion in compact ultrametric spaces
  • Y. Guivarc'h, J. C. Taylor, and L. Ji -- Compactifications of symmetric spaces and positive eigenfunctions of the Laplacian
  • F. Ledrappier -- Some asymptotic properties of random walks on free groups
  • J. C. Taylor -- The Martin compactification associated with a second order strictly elliptic partial differential operator on a manifold \(\mathbf M\)
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