Topics in Probability and Lie Groups : Boundary Theory

ISBN-13: 9780821802755 / Angielski / Miękka / 2001 / 202 str.

Opis

This volume is comprised of two parts: the first contains articles by S.N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (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 Figa-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.