Tata Institute of Fundamental Research 2005; 360 pp; hardcover ISBN10: 8173197032 ISBN13: 9788173197031 List Price: US$40 Member Price: US$32 Order Code: TIFR/8
 Many aspects of the classical probability theory based on vector spaces were generalized in the second half of the twentieth century to measures on groups, especially Lie groups. The subject of probability measures on groups that emerged out of this research has continued to grow and many interesting new developments have occurred in the area in recent years. A School was organized jointly with CIMPA, France and the Tata Institute of Fundamental Research entitled "Probability Measures on Groups: Recent Directions and Trends" in Mumbai. Lecture courses were given at the School by M. Babillot (Orlean, France), D. Bakry (Toulouse, France), S.G. Dani (Tata Institute, Mumbai), J. Faraut (Paris), Y. Guivarc'h (Rennes, France) and M. McCrudden (Manchester, U.K.), aimed at introducing various advanced topics on the theme to students as well as teachers and practicing mathematicians who wanted to get acquainted with the area. The prerequisite for the courses was a basic background in measure theory, harmonic analysis and elementary Lie group theory. The courses were wellreceived. Notes were prepared and distributed to the participants during the courses. The present volume represents improved, edited, and refereed versions of the notes, published for dissemination of the topics to the wider community. It is suitable for graduate students and researchers interested in probability, algebra, and algebraic geometry. A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka. Readership Graduate students and research mathematicians interested in probability, algebra, and algebraic geometry. Table of Contents  M. Babillot  An introduction to Poisson boundaries of Lie groups
 D. Bakry  Functional inequalities for Markov semigroups
 S. G. Dani  Asymptotic behaviour of measures under automorphisms
 J. Faraut  Infinite dimensional harmonic analysis and probability
 Y. Guivarc'h  Limit theorems for random walks and products of random matrices
 M. McCrudden  The embedding problem for probabilities on locally compact groups
