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Quantum Stochastic Processes And Noncommutative Geometry


Quantum Stochastic Processes And Noncommutative Geometry
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Quantum Stochastic Processes And Noncommutative Geometry


Quantum Stochastic Processes And Noncommutative Geometry
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Author : Kalyan B. Sinha
language : en
Publisher:
Release Date : 2007

Quantum Stochastic Processes And Noncommutative Geometry written by Kalyan B. Sinha and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.


The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.



Quantum Stochastic Processes And Noncommutative Geometry


Quantum Stochastic Processes And Noncommutative Geometry
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Author : Kalyan B. Sinha
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-25

Quantum Stochastic Processes And Noncommutative Geometry written by Kalyan B. Sinha and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-25 with Mathematics categories.


The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.



Geometric Science Of Information


Geometric Science Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer
Release Date : 2017-10-30

Geometric Science Of Information written by Frank Nielsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with Computers categories.


This book constitutes the refereed proceedings of the Third International Conference on Geometric Science of Information, GSI 2017, held in Paris, France, in November 2017. The 101 full papers presented were carefully reviewed and selected from 113 submissions and are organized into the following subjects: statistics on non-linear data; shape space; optimal transport and applications: image processing; optimal transport and applications: signal processing; statistical manifold and hessian information geometry; monotone embedding in information geometry; information structure in neuroscience; geometric robotics and tracking; geometric mechanics and robotics; stochastic geometric mechanics and Lie group thermodynamics; probability on Riemannian manifolds; divergence geometry; non-parametric information geometry; optimization on manifold; computational information geometry; probability density estimation; session geometry of tensor-valued data; geodesic methods with constraints; applications of distance geometry.



Group Representations Ergodic Theory And Mathematical Physics


Group Representations Ergodic Theory And Mathematical Physics
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Group Representations Ergodic Theory And Mathematical Physics written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.


George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.



Quantum Stochastics


Quantum Stochastics
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Author : Mou-Hsiung Chang
language : en
Publisher: Cambridge University Press
Release Date : 2015-02-19

Quantum Stochastics written by Mou-Hsiung Chang and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-19 with Language Arts & Disciplines categories.


This book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes for graduate students and researchers. Building a framework that parallels the development of classical probability, it aims to help readers up the steep learning curve of the quantum theory.



Nonlinear Perron Frobenius Theory


Nonlinear Perron Frobenius Theory
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Author : Bas Lemmens
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-03

Nonlinear Perron Frobenius Theory written by Bas Lemmens and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-03 with Mathematics categories.


Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.



Combinatorics Of Minuscule Representations


Combinatorics Of Minuscule Representations
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Author : R. M. Green
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-21

Combinatorics Of Minuscule Representations written by R. M. Green and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.


Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups.



Infinite Dimensional Stochastic Analysis


Infinite Dimensional Stochastic Analysis
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Author : Hui-Hsiung Kuo
language : en
Publisher: World Scientific
Release Date : 2008

Infinite Dimensional Stochastic Analysis written by Hui-Hsiung Kuo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.


This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. 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. Sample Chapter(s). Complex White Noise and the Infinite Dimensional Unitary Group (425 KB). Contents: Complex White Noise and the Infinite Dimensional Unitary Group (T Hida); Complex It Formulas (M Redfern); White Noise Analysis: Background and a Recent Application (J Becnel & A N Sengupta); Probability Measures with Sub-Additive Principal SzegAOCoJacobi Parameters (A Stan); Donsker''s Functional Calculus and Related Questions (P-L Chow & J Potthoff); Stochastic Analysis of Tidal Dynamics Equation (U Manna et al.); Adapted Solutions to the Backward Stochastic NavierOCoStokes Equations in 3D (P Sundar & H Yin); Spaces of Test and Generalized Functions of Arcsine White Noise Formulas (A Barhoumi et al.); An Infinite Dimensional Fourier-Mehler Transform and the L(r)vy Laplacian (K Saito & K Sakabe); The Heat Operator in Infinite Dimensions (B C Hall); Quantum Stochastic Dilation of Symmetric Covariant Completely Positive Semigroups with Unbounded Generator (D Goswami & K B Sinha); White Noise Analysis in the Theory of Three-Manifold Quantum Invariants (A Hahn); A New Explicit Formula for the Solution of the BlackOCoMertonOCoScholes Equation (J A Goldstein et al.); Volatility Models of the Yield Curve (V Goodman). Readership: Graduate-level researchers in stochastic analysis, mathematical physics and financial mathematic



Convexity


Convexity
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Author : Barry Simon
language : en
Publisher: Cambridge University Press
Release Date : 2011-05-19

Convexity written by Barry Simon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-19 with Mathematics categories.


Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.



Rigidity In Higher Rank Abelian Group Actions Volume 1 Introduction And Cocycle Problem


Rigidity In Higher Rank Abelian Group Actions Volume 1 Introduction And Cocycle Problem
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Author : Anatole Katok
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-16

Rigidity In Higher Rank Abelian Group Actions Volume 1 Introduction And Cocycle Problem written by Anatole Katok and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-16 with Mathematics categories.


This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.