Noncommutative Probability

Author : I. Cuculescu,A.G. Oprea
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 41,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401583749

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Noncommutative Probability by I. Cuculescu,A.G. Oprea Pdf

The intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "noncommutative probability" is. So the first decision was not to concentrate on a special topic. For different people, the starting points of such a domain may be different. In what concerns this question, different variants are not discussed. One such variant comes from Quantum Physics. The motivations in this book are mainly mathematical; more precisely, they correspond to the desire of developing a probability theory in a new set-up and obtaining results analogous to the classical ones for the newly defined mathematical objects. Also different mathematical foundations of this domain were proposed. This book concentrates on one variant, which may be described as "von Neumann algebras". This is true also for the last chapter, if one looks at its ultimate aim. In the references there are some papers corresponding to other variants; we mention Gudder, S.P. &al (1978). Segal, I.E. (1965) also discusses "basic ideas".

Author : Dan V. Voiculescu,K. J. Dykema,A. Nica
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 40,9 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821811405

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Free Random Variables by Dan V. Voiculescu,K. J. Dykema,A. Nica Pdf

This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.

Author : Tao Qian,Luigi G. Rodino
Publisher : Springer
Page : 336 pages
File Size : 41,9 Mb
Release : 2016-08-25
Category : Mathematics
ISBN : 9783319419459

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Mathematical Analysis, Probability and Applications – Plenary Lectures by Tao Qian,Luigi G. Rodino Pdf

This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015. The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels. The volume also presents a lecture on the visual exploration of complex functions using the domain coloring technique. Thanks to the accessible style used, readers only need a basic command of calculus.

Author : Luigi Accardi
Publisher : World Scientific
Page : 544 pages
File Size : 53,7 Mb
Release : 1991
Category : Mathematics
ISBN : 9810207166

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Quantum Probability & Related Topics by Luigi Accardi Pdf

This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for this new type of independence is played by the Wigner distribution. This motivated the introduction of new type of quantum independent increments noise, the free noise and the corresponding stochastic calculus. A further generalization, the ?-noises, is discussed. The free stochastic calculus is shown to be able to fit naturally into the general representation free calculus. The basic free are shown to be realized as non-adapted stochastic integrals with respect to the usual Boson white noises. Quantum noise on the finite difference algebra is expressed in terms of the usual Boson white noises. A new quantum way of looking at classical stochastic flows, in particular diffusions on Riemannian Manifolds is explained. Quantum groups are discussed from the point of view of possible applications to quantum probability. The applications of quantum probability to physics are surveyed.

Author : M. Emery,A. Nemirovski,D. Voiculescu
Publisher : Springer
Page : 359 pages
File Size : 50,9 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540450290

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Lectures on Probability Theory and Statistics by M. Emery,A. Nemirovski,D. Voiculescu Pdf

This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during 17th Aug. - 3rd Sept. 1998. The contents of the three courses are the following: - Continuous martingales on differential manifolds. - Topics in non-parametric statistics. - Free probability theory. The reader is expected to have a graduate level in probability theory and statistics. This book is of interest to PhD students in probability and statistics or operators theory as well as for researchers in all these fields. The series of lecture notes from the Saint-Flour Probability Summer School can be considered as an encyclopedia of probability theory and related fields.

Author : Gregory Schehr,Yan V. Fyodorov,Alexander Altland,Neil O'Connell,Leticia F. Cugliandolo
Publisher : Oxford University Press
Page : 641 pages
File Size : 42,7 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198797319

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Stochastic Processes and Random Matrices by Gregory Schehr,Yan V. Fyodorov,Alexander Altland,Neil O'Connell,Leticia F. Cugliandolo Pdf

This text covers in detail recent developments in the field of stochastic processes and Random Matrix Theory. Matrix models have been playing an important role in theoretical physics for a long time and are currently also a very active domain of research in mathematics.

Author : Michael Schürmann,Uwe Franz
Publisher : World Scientific
Page : 548 pages
File Size : 41,7 Mb
Release : 2005-01-12
Category : Science
ISBN : 9789814481021

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Quantum Probability and Infinite Dimensional Analysis by Michael Schürmann,Uwe Franz Pdf

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 : Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
Publisher : Cambridge University Press
Page : 507 pages
File Size : 51,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780521194525

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An Introduction to Random Matrices by Greg W. Anderson,Alice Guionnet,Ofer Zeitouni Pdf

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Author : Nobuaki Obata
Publisher : World Scientific
Page : 447 pages
File Size : 51,5 Mb
Release : 2003-01-16
Category : Mathematics
ISBN : 9789812705242

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Non-commutativity, Infinite-dimensionality and Probability at the Crossroads by Nobuaki Obata Pdf

Infinite-dimensional analysis and quantum probability have undergone significant developments in the last few years and created many applications. This volume includes four expository articles on recent developments in quantum field theory, quantum stochastic differential equations, free probability and quantum white noise calculus, which are targeted also for graduate study. The fourteen research papers deal with most of the current topics, and their interconnections reflect a vivid development in interacting Fock space, infinite-dimensional groups, stochastic independence, non-commutative central limit theorems, stochastic geometry, and so on.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,9 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9789814486507

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Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads by Anonim Pdf

Author : Gordon Blower
Publisher : Cambridge University Press
Page : 448 pages
File Size : 40,7 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9781139481953

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Random Matrices: High Dimensional Phenomena by Gordon Blower Pdf

This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.

Author : M. M. Rao
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220541

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Real and Stochastic Analysis by M. M. Rao Pdf

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.

Author : 野水克己
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 43,9 Mb
Release : 2001
Category : Mathematical analysis
ISBN : 0821827804

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Selected Papers on Classical Analysis by 野水克己 Pdf

This volume contains papers that originally appeared in Japanese in the journal Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers here are in the general area of mathematical analysis as it pertains to free probability theory.

Author : Percy Deift,Peter Forrester
Publisher : Cambridge University Press
Page : 539 pages
File Size : 50,5 Mb
Release : 2014-12-15
Category : Language Arts & Disciplines
ISBN : 9781107079922

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Random Matrix Theory, Interacting Particle Systems and Integrable Systems by Percy Deift,Peter Forrester Pdf

This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.

Author : Rongwei Yang
Publisher : Springer Nature
Page : 277 pages
File Size : 49,9 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031516054

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A Spectral Theory Of Noncommuting Operators by Rongwei Yang Pdf