نظریهٔ احتمال آزاد (مکاتبات مؤسسهٔ فیلدز)

Contribution by Michael Douglas only. Large N QFT and Matrix Models Free Probability Theory Is A Highly Noncommutative Probability Theory, With Independence Based On Free Products Instead Of Tensor Products. The Theory Models Random Matrices In The Large N Limit And Operator Algebra Free Products. It Has Led To A Surge Of New Results On The Von Neumann Algebras Of Free Groups. This Is A Volume Of Papers From A Workshop On Random Matrices And Operator Algebra Free Products, Held At The Fields Institute For Research In The Mathematical Sciences In March 1995. Over The Last Few Years, There Has Been Much Progress On The Operator Algebra And Noncommutative Probability Sides Of The Subject. New Links With The Physics Of Masterfields And The Combinatorics Of Noncrossing Partitions Have Emerged. Moreover There Is A Growing Free Entropy Theory. The Idea Of This Workshop Was To Bring Together People Working In All These Directions And From An Even Broader Free Products Area Where Future Developments Might Lead. Free Brownian Motion, Free Stochastic Calculus And Random Matrices / Philippe Biane -- Large N Quantum Field Theory And Matrix Models / Michael R. Douglas -- Free Products Of Finite Dimensional And Other Von Neumann Algebras With Respect To Non-tracial States / Kenneth J. Dykema -- Amalgamated Free Product C*-algebras And Kk-theory / Emmanuel Germain -- Connexion Coefficients For The Symmetric Group, Free Products In Operator Algebras And Random Matrices / Ian P. Goulden And David M. Jackson -- On Voiculescu's R- And S-transforms For Free Non-commuting Random Variables / Uffe Haagerup -- R-diagonal Pairs -- A Common Approach To Haar Unitaries And Circular Elements / Alexandru Nica And Roland Speicher -- A Class Of C*-algebras Generalizing Both Cuntz-krieger Algebras And Crossed Products By Z / Michael V. Pimsner -- An Invariant For Subfactors In The Von Neumann Algebra Of A Free Group / Florin Radulescu. Dan-virgil Voiculescu, Editor. Papers From A Workshop On Random Matrices And Operator Algebra Free Products Held Mar. 1995 At The Fields Institute. Includes Bibliographical References.