Softcover ISBN:  9780821802755 
Product Code:  CRMP/28 
List Price:  $77.00 
MAA Member Price:  $69.30 
AMS Member Price:  $61.60 
Electronic ISBN:  9781470439422 
Product Code:  CRMP/28.E 
List Price:  $72.00 
MAA Member Price:  $64.80 
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Book DetailsCRM Proceedings & Lecture NotesVolume: 28; 2001; 202 ppMSC: Primary 60; Secondary 31; 22;
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.ReadershipGraduate students and research mathematicians interested in probability theory and stochastic processes.

Table of Contents

Chapters

Heat kernel and Green function estimates on noncompact symmetric spaces. II

Local fields, Gaussian measures, and Brownian motions

An application of Gelfand pairs to a problem of diffusion in compact ultrametric spaces

Compactifications of symmetric spaces and positive eigenfunctions of the Laplacian

Some asymptotic properties of random walks on free groups

The Martin compactification associated with a second order strictly elliptic partial differential operator on a manifold $\textbf M$


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

Chapters

Heat kernel and Green function estimates on noncompact symmetric spaces. II

Local fields, Gaussian measures, and Brownian motions

An application of Gelfand pairs to a problem of diffusion in compact ultrametric spaces

Compactifications of symmetric spaces and positive eigenfunctions of the Laplacian

Some asymptotic properties of random walks on free groups

The Martin compactification associated with a second order strictly elliptic partial differential operator on a manifold $\textbf M$