Download or read book The Semicircle Law Free Random Variables and Entropy written by Fumio Hiai and published by American Mathematical Soc.. This book was released on 2000 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This book brings together both new material and recent surveys on some topics in differential equations that are either directly relevant to, or closely associated with, mathematical physics. Its topics include asymptotic formulas for the ground-state energy of fermionic gas, renormalization ideas in quantum field theory from perturbations of the free Hamiltonian on the circle, $J$-selfadjoint Dirac operators, spectral theory of Schrodinger operators, inverse problems, isoperimetric inequalities in quantum mechanics, Hardy inequalities, and non-adiabatic transitions. Excellent survey articles on Dirichlet-Neumann inverse problems on manifolds (by Uhlmann), numerical investigations associated with Laplacian eigenvalues on planar regions (by Trefethen), Snell's law and propagation of singularities in the wave equation (by Vasy), random operators on tree graphs (by Aizenmann) make this book interesting and valuable for graduate students, young mathematicians, and physicists alike.
Download or read book Free Probability and Random Matrices written by James A. Mingo and published by Springer. This book was released on 2017-06-24 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Download or read book Fundamental Aspects Of Quantum Physics Proceedings Of The Japan italy Joint Workshop On Quantum Open Systems Quantum Chaos And Quantum Measurement written by Shuichi Tasaki and published by World Scientific. This book was released on 2003-02-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes new topics such as the stochastic limit approach to nonequilibrium states, a new algebraic approach to relativistic nonequilibrium local states, classical and quantum features of weak chaos, transports in quantum billiards, the Welcher-Weg puzzle with a decaying atom, and the topics related to the quantum Zeno effect.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Download or read book Fundamental Aspects of Quantum Physics written by Luigi Accardi and published by World Scientific. This book was released on 2003 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes new topics such as the stochastic limit approach to nonequilibrium states, a new algebraic approach to relativistic nonequilibrium local states, classical and quantum features of weak chaos, transports in quantum billiards, the Welcher-Weg puzzle with a decaying atom, and the topics related to the quantum Zeno effect.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Download or read book XI Symposium on Probability and Stochastic Processes written by Ramsés H. Mena and published by Birkhäuser. This book was released on 2015-07-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features a collection of contributed articles and lecture notes from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes.
Download or read book Levy Processes Integral Equations Statistical Physics Connections and Interactions written by Lev A. Sakhnovich and published by Springer Science & Business Media. This book was released on 2012-07-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.
Download or read book High dimensional Manifold Topology Proceedings Of The School written by F Thomas Farrell and published by World Scientific. This book was released on 2003-10-17 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.)Equivariant Cellular Homology and Its Applications (B Chorny)Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.)Chain Complex Invariants for Group Actions (L E Jones)The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.)The Surgery Exact Sequence Revisited (E K Pedersen)K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer)Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz)and other papers Readership: Graduate students and researchers in geometry and topology. Keywords:High-Dimensional Manifold Topology;Operator Algebras;K-Theory;L-Theory;Foliated Control Theory
Download or read book High dimensional Manifold Topology written by R. T. Farrell and published by World Scientific. This book was released on 2003 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers topics such as manifolds with positive scalar curvature, pseudo-isotopy spectrum and controlled theory, and reduction of the Novikov and Borel conjectures for aspherical complexes to aspherical manifolds.
Download or read book High dimensional Manifold Topology written by Abdus Salam International Centre for Theoretical Physics and published by World Scientific. This book was released on 2003 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.); Equivariant Cellular Homology and Its Applications (B Chorny); Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.); Chain Complex Invariants for Group Actions (L E Jones); The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.); The Surgery Exact Sequence Revisited (E K Pedersen); K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer); Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz); and other papers;
Download or read book Eigenvalue Distribution of Large Random Matrices written by Leonid Andreevich Pastur and published by American Mathematical Soc.. This book was released on 2011 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
Download or read book Infinite Dimensional Analysis Quantum Probability And Related Topics Qp38 Proceedings Of The International Conference written by Noboru Watanabe and published by World Scientific. This book was released on 2023-10-25 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to return to the starting point of the fields of infinite dimensional analysis and quantum probability, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics including classical probability and to different branches of physics, in particular, research for new paradigms for information science on the basis of quantum theory.
Download or read book Selected Papers on Analysis and Related Topics written by and published by American Mathematical Soc.. This book was released on 2008 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains translations of papers that originally appeared in the Japanese journal 'Sugaku'. The papers range over a variety of topics, including operator algebras, analysis, and statistics.
Download or read book Random Matrices and Non Commutative Probability written by Arup Bose and published by CRC Press. This book was released on 2021-10-26 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Probability And Infinite Dimensional Analysis From Foundations To Appllications written by Uwe Franz and published by World Scientific. This book was released on 2005-01-12 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.
Download or read book Quantification of Uncertainty Improving Efficiency and Technology written by Marta D'Elia and published by Springer Nature. This book was released on 2020-07-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores four guiding themes – reduced order modelling, high dimensional problems, efficient algorithms, and applications – by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the book’s content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.
Download or read book Computation and Combinatorics in Dynamics Stochastics and Control written by Elena Celledoni and published by Springer. This book was released on 2019-01-13 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.
