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Author : Łukasz Wojakowski
Publisher : Unknown
Page : 56 pages
File Size : 42,7 Mb
Release : 2007
Category : Free probability theory
ISBN : PSU:000061623149
Author : Luigi Accardi,Wolfgang Freudenberg,Michael Schurmann
Publisher : World Scientific
Page : 392 pages
File Size : 50,6 Mb
Release : 2007-07-12
Category : Mathematics
ISBN : 9789814474795
This volume contains the latest results in the fields of quantum probability and infinite dimensional analysis. The contributions range from classical probability, 'pure' functional analysis and foundations of quantum mechanics to applications in mathematical physics, quantum information theory and modern mathematical finance. This diversity illustrates that research in quantum probability and infinite dimensional analysis is very active and strongly involved in modern mathematical developments and applications.
Author : Arup Bose
Publisher : CRC Press
Page : 420 pages
File Size : 55,7 Mb
Release : 2021-10-26
Category : Mathematics
ISBN : 9781000458824
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Author : Henryk Gacki
Publisher : Unknown
Page : 68 pages
File Size : 50,6 Mb
Release : 2007
Category : Dynamics
ISBN : PSU:000061570993
Author : Camille Male
Publisher : American Mathematical Society
Page : 88 pages
File Size : 45,9 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470442989
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.
Author : Daniel Alpay,Mihaela B. Vajiac
Publisher : Springer
Page : 316 pages
File Size : 45,9 Mb
Release : 2019-08-08
Category : Mathematics
ISBN : 9783030184841
This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.
Author : Michael Schürmann,Uwe Franz
Publisher : World Scientific
Page : 548 pages
File Size : 53,5 Mb
Release : 2005-01-12
Category : Science
ISBN : 9789814481021
This volume collects research papers in quantum probability and related fields and reflects the recent developments in quantum probability ranging from the foundations to its applications. Contents:Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.)Generating Function Method for Orthogonal Polynomials and Jacobi–Szegö Parameters (N Asai et al.)Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V P Belavkin & C R Williams)A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A C R Belton)Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & J M Lindsay)Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Lévy Processes (V K Dobrev et al.)On Algebraic and Quantum Random Walks (D Ellinas)Dual Representations for the Schrödinger Algebra (P Feinsilver & R Schott)A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.)On Quantum Logical Gates on a General Fock Space (W Freudenberg et al.)On an Argument of David Deutsch (R Gill)The Method of Double Product Integrals in Quantisation of Lie Bialgebras (R L Hudson)Asymptotics of Large Truncated Haar Unitary Matrices (J L Réffy)Three Ways to Representations of BA(E) (M Skeide)On Topological Entropy of Quotients and Extensions (J Zacharias)and other papers Readership: Researchers in the fields of probability, mathematical physics and functional analysis. Keywords:Quantum Probability;Infinite Dimensional Analysis;Mathematical Physics;Lévy Processes;Interacting Fock Space;Quantum Markov ProcessesKey Features:Reflects recent developments in the fieldsAll the articles are contributed by renowned researchers
Author : Rolando Rebolledo
Publisher : World Scientific
Page : 339 pages
File Size : 47,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814338745
This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
Author : Marek Bożejko,Wojciech Młotkowski,Janusz Wysoczański
Publisher : Unknown
Page : 476 pages
File Size : 53,6 Mb
Release : 2006
Category : Probabilities
ISBN : UOM:39015069190877
Author : Akihito Hora,Nobuaki Obata
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 51,6 Mb
Release : 2007-07-05
Category : Science
ISBN : 9783540488637
This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Author : Anonim
Publisher : Unknown
Page : 436 pages
File Size : 41,5 Mb
Release : 2008
Category : Mathematics
ISBN : UCSD:31822036065647
Author : Anonim
Publisher : Unknown
Page : 416 pages
File Size : 54,9 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015072605523
Author : Victor Dévoué
Publisher : Unknown
Page : 78 pages
File Size : 40,9 Mb
Release : 2007
Category : Wave equation
ISBN : STANFORD:36105124212932
Author : Marek Bożejko
Publisher : Unknown
Page : 334 pages
File Size : 43,9 Mb
Release : 2007
Category : Free probability theory
ISBN : UOM:39015075633761
Author : Fumio Hiai,Dénes Petz
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 51,7 Mb
Release : 2006-03-23
Category : Mathematics
ISBN : 9780821841358
The book treats free probability theory, which has been extensively developed since the early 1980s. The emphasis is put on entropy and the random matrix model approach. The volume is a unique presentation demonstrating the extensive interrelation between the topics. Wigner's theorem and its broad generalizations, such as asymptotic freeness of independent matrices, are explained in detail. Consistent throughout the book is the parallelism between the normal and semicircle laws. Voiculescu's multivariate free entropy theory is presented with full proofs and extends the results to unitary operators. Some applications to operator algebras are also given. Based on lectures given by the authors in Hungary, Japan, and Italy, the book is a good reference for mathematicians interested in free probability theory and can serve as a text for an advanced graduate course.