**CRM Proceedings & Lecture Notes**

Volume: 28;
2001;
202 pp;
Softcover

MSC: Primary 60;
Secondary 31; 22

Print ISBN: 978-0-8218-0275-5

Product Code: CRMP/28

List Price: $72.00

Individual Member Price: $57.60

**Electronic ISBN: 978-1-4704-3942-2
Product Code: CRMP/28.E**

List Price: $72.00

Individual Member Price: $57.60

# Topics in Probability and Lie Groups: Boundary Theory

Share this page *Edited by *
*J. C. Taylor*

A co-publication of the AMS and Centre de Recherches Mathématiques

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.

#### Readership

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

# Table of Contents

## Topics in Probability and Lie Groups: Boundary Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Heat kernel and Green function estimates on noncompact symmetric spaces. II 112
- Local fields, Gaussian measures, and Brownian motions 1122
- An application of Gelfand pairs to a problem of diffusion in compact ultrametric spaces 5162
- Compactifications of symmetric spaces and positive eigenfunctions of the Laplacian 6980
- Some asymptotic properties of random walks on free groups 117128
- The Martin compactification associated with a second order strictly elliptic partial differential operator on a manifold 𝑀 153164
- Back Cover Back Cover1214