Noncommutative Distributions

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Noncommutative Distributions

Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani
Noncommutative Distributions Book PDF

Author : Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani
Publisher : CRC Press
Page : 216 pages
File Size : 49,6 Mb
Release : 1993-08-26
Category : Mathematics
ISBN : 0824791312

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Noncommutative Distributions by Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani Pdf

Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines.

Noncommutative Distributions

Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani
Noncommutative Distributions Book PDF

Author : Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani
Publisher : CRC Press
Page : 207 pages
File Size : 45,7 Mb
Release : 1993-08-26
Category : Mathematics
ISBN : 9781482277579

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Noncommutative Distributions by Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani Pdf

Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary st

Noncommutative Geometry

Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Noncommutative Geometry Book PDF

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 54,5 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540203575

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence

Camille Male
Traffic Distributions and Independence Permutation Invariant Random Matrices and the Three Notions of Independence Book PDF

Author : Camille Male
Publisher : American Mathematical Society
Page : 88 pages
File Size : 41,7 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470442989

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Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence by Camille Male Pdf

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.

Noncommutative Geometry

Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Noncommutative Geometry Book PDF

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer
Page : 364 pages
File Size : 45,8 Mb
Release : 2003-12-15
Category : Mathematics
ISBN : 9783540397021

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Non-commutative Cryptography and Complexity of Group-theoretic Problems

Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Non commutative Cryptography and Complexity of Group theoretic Problems Book PDF

Author : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 50,7 Mb
Release : 2011
Category : Computers
ISBN : 9780821853603

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Non-commutative Cryptography and Complexity of Group-theoretic Problems by Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov Pdf

Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.

Noncommutative Geometry, Quantum Fields and Motives

Alain Connes,Matilde Marcolli
Noncommutative Geometry Quantum Fields and Motives Book PDF

Author : Alain Connes,Matilde Marcolli
Publisher : American Mathematical Soc.
Page : 785 pages
File Size : 45,8 Mb
Release : 2019-03-13
Category : Electronic
ISBN : 9781470450458

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Noncommutative Geometry, Quantum Fields and Motives by Alain Connes,Matilde Marcolli Pdf

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.

Free Random Variables

Dan V. Voiculescu,K. J. Dykema,A. Nica
Free Random Variables Book PDF

Author : Dan V. Voiculescu,K. J. Dykema,A. Nica
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 43,6 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.

Ecole d'Ete de Probabilites de Saint-Flour XXVIII, 1998

M. Emery,Arkadiĭ Semenovich Nemirovskiĭ,Dan V. Voiculescu,D. Voiculescu
Ecole d Ete de Probabilites de Saint Flour XXVIII 1998 Book PDF

Author : M. Emery,Arkadiĭ Semenovich Nemirovskiĭ,Dan V. Voiculescu,D. Voiculescu
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 47,5 Mb
Release : 2000-06-26
Category : Mathematics
ISBN : 3540677364

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Ecole d'Ete de Probabilites de Saint-Flour XXVIII, 1998 by M. Emery,Arkadiĭ Semenovich Nemirovskiĭ,Dan V. Voiculescu,D. Voiculescu Pdf

MSC 2000: 46L10, 46L53

Trace Formulas

Steven Lord,Edward McDonald,Fedor Sukochev,Dmitriy Zanin
Trace Formulas Book PDF

Author : Steven Lord,Edward McDonald,Fedor Sukochev,Dmitriy Zanin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 43,5 Mb
Release : 2023-04-03
Category : Mathematics
ISBN : 9783110700176

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Trace Formulas by Steven Lord,Edward McDonald,Fedor Sukochev,Dmitriy Zanin Pdf

This volume introduces noncommutative integration theory on semifinite von Neumann algebras and the theory of singular traces for symmetric operator spaces. Deeper aspects of the association between measurability, poles and residues of spectral zeta functions, and asymptotics of heat traces are studied. Applications in Connes’ noncommutative geometry that are detailed include integration of quantum differentials, measures on fractals, and Connes’ character formula concerning the Hochschild class of the Chern character.

Quantum Symmetries

Guillaume Aubrun,Adam Skalski,Roland Speicher
Quantum Symmetries Book PDF

Author : Guillaume Aubrun,Adam Skalski,Roland Speicher
Publisher : Springer
Page : 119 pages
File Size : 49,6 Mb
Release : 2017-10-11
Category : Mathematics
ISBN : 9783319632063

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Quantum Symmetries by Guillaume Aubrun,Adam Skalski,Roland Speicher Pdf

Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.

Statistics of Knots and Entangled Random Walks

S K Nechaev
Statistics of Knots and Entangled Random Walks Book PDF

Author : S K Nechaev
Publisher : World Scientific
Page : 204 pages
File Size : 55,9 Mb
Release : 1996-09-03
Category : Science
ISBN : 9789814499507

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Statistics of Knots and Entangled Random Walks by S K Nechaev Pdf

In this book, the author announces the class of problems called “entropy of knots” and gives an overview of modern physical applications of existing topological invariants. He constructs statistical models on knot diagrams and braids using the representations of Jones–Kauffman and Alexander invariants and puts forward the question of limit distribution of these invariants for randomly generated knots. The relation of powers of corresponding algebraic invariants to the Lyapunov exponents of the products of noncommutative matrices is described. Also the problem of conditional joint limit distributions for “brownian bridges” on braids is discussed. Special cases of noncommutative groups PSL(2,R), PSL(2,Z) and braid groups are considered in detail. In this volume, the author also discusses the application of conformal methods for explicit construction of topological invariants for random walks on multiconnected manifolds. The construction of these topological invariants and the monodromy properties of correlation function of some conformal theories are also discussed. The author also considers the physical applications of “knot entropy” problem in various physical systems, focussing on polymers. Contents:Knot Diagrams as Disordered Spin Systems:Introduction: Statistical Problems in TopologyReview of Abelian Problems in Statistics of Entangled Random Walks and Incompleteness of Gauss InvariantNonabelian Algebraic Knot InvariantsLattice Knot Diagrams as Disordered Potts ModelAnnealed and Quenched Realizations of Topological DisorderRandom Walks on Local Noncommutative Groups:IntroductionBrownian Bridges on Simplest Noncommutative Groups and Knot StatisticsRandom Walks on Locally Free GroupsBrownian Bridges on Lobachevskii Plane and Products of Noncommutative Random MatricesConformal Methods in Statistics of Entangled Random Walks:Introduction: Random Walk with Topological ConstraintsConstruction of Nonabelian Connections for Γ2 and PSL(2,Z) from Conformal MethodsRandom Walk on Double Punctured Plane and Conformal Field TheoryStatistics of Random Walks with Topological Constraints in 2D Lattice of ObstaclesPhysical Applications:Introduction: Polymer Language in Statistics of Entangled Chain-Like ObjectsPolymer Chain in 3D Array of Obstacles: Critical Exponents for Gyration RadiusHigh Elasticity of Polymer NetworksCollapsed Phase of Unknotted PolymerOrdering Phase Transition in Entangled “Directed Polymers” Readership: Mathematicians, mathematical physicists and polymer physicists. keywords:Knots;Topological Invariants;Kauffman;Knot Entropy;Polymers;Mathematical Physicists;Polymer Physicists

Operator Theory, Functional Analysis and Applications

M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Operator Theory Functional Analysis and Applications Book PDF

Author : M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Publisher : Springer Nature
Page : 654 pages
File Size : 49,9 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030519452

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Operator Theory, Functional Analysis and Applications by M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich Pdf

This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Probabilistic Methods in Combinatorial Analysis

Vladimir N. Sachkov
Probabilistic Methods in Combinatorial Analysis Book PDF

Author : Vladimir N. Sachkov
Publisher : Cambridge University Press
Page : 260 pages
File Size : 46,5 Mb
Release : 1997-05-15
Category : Mathematics
ISBN : 9780521455121

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Probabilistic Methods in Combinatorial Analysis by Vladimir N. Sachkov Pdf

This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these define the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.

Non-Associative and Non-Commutative Algebra and Operator Theory

Cheikh Thiécoumbe Gueye,Mercedes Siles Molina
Non Associative and Non Commutative Algebra and Operator Theory Book PDF

Author : Cheikh Thiécoumbe Gueye,Mercedes Siles Molina
Publisher : Springer
Page : 254 pages
File Size : 49,5 Mb
Release : 2016-11-21
Category : Mathematics
ISBN : 9783319329024

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Non-Associative and Non-Commutative Algebra and Operator Theory by Cheikh Thiécoumbe Gueye,Mercedes Siles Molina Pdf

Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he has served as a mentor to a generation of mathematicians in Senegal and around the world.