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Random Operator Theory

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Random Operator Theory

Random Operator Theory Book
Author : Reza Saadati
Publisher : Academic Press
Release : 2016-08-24
ISBN : 0081009550
Language : En, Es, Fr & De

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Book Description :

Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications. Explores random differentiation and random integral equations Delves into the study of random operator theory Discusses the concept of random Banach algebras and its applications

Random Operators

Random Operators Book
Author : Michael Aizenman,Simone Warzel
Publisher : American Mathematical Soc.
Release : 2015-12-11
ISBN : 1470419130
Language : En, Es, Fr & De

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Book Description :

This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Random Integral Equations

Random Integral Equations Book
Author : Bharucha-Reid
Publisher : Academic Press
Release : 1973-03-02
ISBN : 008095605X
Language : En, Es, Fr & De

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Random Integral Equations

Spectral Theory of Random Schr dinger Operators

Spectral Theory of Random Schr  dinger Operators Book
Author : R. Carmona,J. Lacroix
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461244889
Language : En, Es, Fr & De

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Book Description :

Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.

Random Operator Theory

Random Operator Theory Book
Author : Reza Saadati
Publisher : Academic Press
Release : 2016-08-17
ISBN : 9780128053461
Language : En, Es, Fr & De

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Book Description :

"Random Operator Theory" provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications. Explores random differentiation and random integral equationsDelves into the study of random operator theoryDiscusses the concept of random Banach algebras and its applications

Recent Trends in Operator Theory and Partial Differential Equations

Recent Trends in Operator Theory and Partial Differential Equations Book
Author : Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland
Publisher : Birkhäuser
Release : 2017-02-23
ISBN : 3319470795
Language : En, Es, Fr & De

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Book Description :

This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.

Random Linear Operators

Random Linear Operators Book
Author : A.V. Skorohod
Publisher : Springer Science & Business Media
Release : 2001-11-30
ISBN : 9781402003264
Language : En, Es, Fr & De

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Book Description :

It isn't that they can't see Approach your problems from the solution. the right end and begin with It is that they can't see the the answers. Then one day, perhaps you will find the problem. final question. G. K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze l1urders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Eigenvalue Distribution of Large Random Matrices

Eigenvalue Distribution of Large Random Matrices Book
Author : Leonid Andreevich Pastur,Mariya Shcherbina
Publisher : American Mathematical Soc.
Release : 2011
ISBN : 082185285X
Language : En, Es, Fr & De

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Book Description :

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.

Nonlinear Operator Theory in Probablistic Metric Spaces

Nonlinear Operator Theory in Probablistic Metric Spaces Book
Author : Shih-sen Chang,Yeol Je Cho,Sin-min Kang
Publisher : Nova Publishers
Release : 2001
ISBN : 9781560729808
Language : En, Es, Fr & De

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Book Description :

The purpose of this book is to give a comprehensive introduction to the study of non-linear operator theory in probabilistic metric spaces. This book is introduced as a survey of the latest and new results on the following topics: Basic theory of probabilistic metric spaces; Fixed point theorems for single-valued and multi-valued mappings in probabilistic metric spaces; Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces; Coincidence point theorems, minimisation and fixed degree theorems in probabilistic metric spaces; Probabilistic contractors, accretive mappings and topological degree in probabilistic normed spaces; Nonlinear semigroups and differential equations in probabilistic metric spaces; KKM theorems, minimax theorems and variational inequalities.

Operator Theory with a Random Potential and Some Questions of Statistical Physics

Operator Theory with a Random Potential  and Some Questions of Statistical Physics Book
Author : Viktor Nikolaevich Popov
Publisher : American Mathematical Soc.
Release : 1991
ISBN : 9780821831397
Language : En, Es, Fr & De

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Book Description :

This collection is devoted to problems of operator theory with a random potential and a number of problems of statistical physics. For the Schrodinger operator with a potential randomly depending on time, mean wave operators, and the mean scattering operator are computed, and it is shown that the averaged dynamics behaves like free dynamics in the limit of infinite time. Results of applying the method of functional integration to some problems of statistical physics are presented: the theory of systems with model Hamiltonians and their dynamics, ferromagnetic systems of spin 1/2, Coulomb and quantum crystals. This collection is intended for specialists in spectral theory and statistical physics.

Spectral Operator Theory and Related Topics

Spectral Operator Theory and Related Topics Book
Author : Vladimir Aleksandrovich Marchenko
Publisher : American Mathematical Soc.
Release : 1994
ISBN : 9780821841228
Language : En, Es, Fr & De

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Book Description :

"The collection contains the papers of mathematicians who are participants of the seminar on Mathematical Physics in Kharkov, Ukraine. The papers are mainly devoted to nontraditional problems of spectral theory, of disordered systems, to the spectral aspects of homogenization, and of properties of ergodic dynamical systems."--ABSTRACT.

Free Probability and Random Matrices

Free Probability and Random Matrices Book
Author : James A. Mingo,Roland Speicher
Publisher : Springer
Release : 2017-06-24
ISBN : 1493969420
Language : En, Es, Fr & De

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Book Description :

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.

Spectra of Random and Almost Periodic Operators

Spectra of Random and Almost Periodic Operators Book
Author : Leonid Pastur,Alexander Figotin
Publisher : Springer
Release : 2011-12-10
ISBN : 9783642743481
Language : En, Es, Fr & De

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Book Description :

In the last fifteen years the spectral properties of the Schrodinger equation and of other differential and finite-difference operators with random and almost-periodic coefficients have attracted considerable and ever increasing interest. This is so not only because of the subject's position at the in tersection of operator spectral theory, probability theory and mathematical physics, but also because of its importance to theoretical physics, and par ticularly to the theory of disordered condensed systems. It was the requirements of this theory that motivated the initial study of differential operators with random coefficients in the fifties and sixties, by the physicists Anderson, 1. Lifshitz and Mott; and today the same theory still exerts a strong influence on the discipline into which this study has evolved, and which will occupy us here. The theory of disordered condensed systems tries to describe, in the so-called one-particle approximation, the properties of condensed media whose atomic structure exhibits no long-range order. Examples of such media are crystals with chaotically distributed impurities, amorphous substances, biopolymers, and so on. It is natural to describe the location of atoms and other characteristics of such media probabilistically, in such a way that the characteristics of a region do not depend on the region's position, and the characteristics of regions far apart are correlated only very weakly. An appropriate model for such a medium is a homogeneous and ergodic, that is, metrically transitive, random field.

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities Book
Author : George Xian-Zhi Yuan
Publisher : American Mathematical Soc.
Release : 1998
ISBN : 0821807471
Language : En, Es, Fr & De

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Book Description :

This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given. This work: presents new results and recent development of KKM theory; offers an overview of modern and up-to-date treatment of the KKM theory, including related articles covering theory and applications; uses an interdisciplinary approach with specific applications in mathematics and economics; and, includes a comprehensive bibliography.

Products of Random Matrices with Applications to Schr dinger Operators

Products of Random Matrices with Applications to Schr  dinger Operators Book
Author : P. Bougerol,Lacroix
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1468491725
Language : En, Es, Fr & De

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Book Description :

CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties . 190 3. Slowly increasing generalized eigenfunctions 195 4. Approximations of the spectral measure 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P.

Non Linear Mathematics Vol II

Non Linear Mathematics Vol  II Book
Author : Thomas L. Saaty
Publisher : RWS Publications
Release : 2014-12-22
ISBN : 1888603399
Language : En, Es, Fr & De

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Book Description :

Nonlinear equations have existed for hundreds of years; their systematic study, however, is a relatively recent phenomenon. This volume, together with its companion', Nonlinear Matliematics Vol. I, provides exceptionally comprehensive coverage of this recently formed area of study. It encompasses both older and more recent developments in the field of equations, with particular emphasis on nonlinear equations because, as Professor Saaty maintains, "that is what is needed today." Together the two volumes cover all the major types of classical equations (except partial differential equations, which require a separate volume). This volume includes material on seven types: operator equations, functional equations, difference equations, delay-differential equations, integral equations, integro-differential equations and stochastic differential equations. Special emphasis is placed on linear and nonlinear equations in function spaces and On general methods of solving different types of such equations. Above all, this book is practical. It reviews the variety of existing types of equations and provides methods for their solution. It is meant to help the reader acquire new methods for formulating problems. Its clear organization and copious references make it suitable for graduate students as well as scientists, technologists and mathematicians.

Proceedings of the Seventh Conference on Probability Theory

Proceedings of the Seventh Conference on Probability Theory Book
Author : Anonim
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2020-05-28
ISBN : 3112314034
Language : En, Es, Fr & De

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Book Description :

Download Proceedings of the Seventh Conference on Probability Theory book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Library of Congress Subject Headings

Library of Congress Subject Headings Book
Author : Library of Congress,Library of Congress. Subject Cataloging Division,Library of Congress. Office for Subject Cataloging Policy
Publisher : Unknown
Release : 1994
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Library of Congress Subject Headings book written by Library of Congress,Library of Congress. Subject Cataloging Division,Library of Congress. Office for Subject Cataloging Policy, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Stochastic Processes in Mathematical Physics and Engineering

Stochastic Processes in Mathematical Physics and Engineering Book
Author : Richard Bellman
Publisher : American Mathematical Soc.
Release : 1964
ISBN : 0821813161
Language : En, Es, Fr & De

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Book Description :

Download Stochastic Processes in Mathematical Physics and Engineering book written by Richard Bellman, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Foundations of the Probabilistic Mechanics of Discrete Media

Foundations of the Probabilistic Mechanics of Discrete Media Book
Author : D. R. Axelrad
Publisher : Elsevier
Release : 2016-03-16
ISBN : 1483285723
Language : En, Es, Fr & De

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Book Description :

This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of such variables. Hence the probabilistic mechanics of discrete media are based on the mathematical theory of probability and the axiomatics of measure theory.