CRM Proceedings & Lecture Notes 2001; 202 pp; softcover Volume: 28 ISBN10: 0821802755 ISBN13: 9780821802755 List Price: US$72 Member Price: US$57.60 Order Code: CRMP/28
 This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and FigàTalomanaca. 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 pre1992 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 FigàTalamanca 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 selfcontained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership 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. FigàTalamanca  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 \(\mathbf M\)
