Combinatorial theory of the free product with amalgamation and operator-valued free probability theory / / Roland Speicher

• Record Nr.: UNINA9910788734003321
• Autore: Speicher Roland <1960->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [1998]; ©1998
• ISBN: 1-4704-0216-5
• Descrizione fisica: 1 online resource (105 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 627
• Disciplina: 510 s; 512/.55
• Soggetti: Operator-valued functions; Selfadjoint operators; Free products (Group theory); Combinatorial analysis; Free probability theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "March 1998, volume 132, number 627 (third of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Introduction""; ""Chapter I. Preliminaries on non-crossing partitions""; ""1.1. Non-crossing partitions""; ""1.2. Incidence algebra and convolution""; ""1.3. Multiplicative functions""; ""Chapter II. Operator-valued multiplicative functions on the lattice of non-crossing partitions""; ""2.1. Operator-valued multiplicative functions""; ""2.2. Connection between f and f â??C""; ""2.3. Special case I = I(C,C)""; ""2.4. Tracial multiplicative functions""; ""2.5. Product and cluster property""; ""Chapter III. Amalgamated free products""; ""3.1. Basic notations""; ""3.2. Moment and cumulant functions""""3.3. Definition of the amalgamated free product""; ""3.4. Explicit formula for α[sub(1)] â??α[sub(2)]""; ""3.5. Positivity of the amalgamated free product""; ""Chapter IV. Operator-valued free probability theory""; ""4.1. B-valued random variables and free convolution""; ""4.2. B-Gaussian distributions and central limit theorem""; ""4.3. Positivity of B-Gaussian distributions""; ""4.4. Compound B-Poisson distributions""; ""4.5. Infinitely divisible distributions""; ""4.6. Full Fock space over a Hilbert-B-bimodule""; ""4.7. Realization of infinitely divisible distributions on a full Fock space""""Chapter V. Operator-valued stochastic processes and stochastic differential equations""; ""5.1. B-valued stochastic processes""; ""5.2. Formulation of the problem""; ""5.3. Possible solutions of the problem""; ""5.4. Gaussian approximation""; ""Bibliography""