Memoirs of the American Mathematical Society 1998; 88 pp; softcover Volume: 132 ISBN10: 0821806939 ISBN13: 9780821806937 List Price: US$48 Individual Members: US$28.80 Institutional Members: US$38.40 Order Code: MEMO/132/627
 Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows reproving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of "freeness". This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges. Readership Graduate students, research mathematicians and physicists working in functional analysis. Table of Contents  Preliminaries on noncrossing partitions
 Operatorvalued multiplicative functions on the lattice of noncrossing partitions
 Amalgamated free products
 Operatorvalued free probability theory
 Operatorvalued stochastic processes and stochastic differential equations
 Bibliography
