Download or read book Random Operator Theory written by Reza Saadati and published by Academic Press. This book was released on 2016-08-24 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Random Operators written by Michael Aizenman and published by American Mathematical Soc.. This book was released on 2015-12-11 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Solution of Random Operator Equations and Inclusions written by Ismat Beg and published by LAP Lambert Academic Publishing. This book was released on 2011-02 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in probabilistic operator theory generally includes the solutions of random operator equations and random operator inclusion, random extension theorems, limit theorems, measure theoretic problems, spectral theory of random operators and semi groups of random operators and their properties. Various ideas associated with random fixed point theory are used to form a particularly elegant approach for the solution of nonlinear random systems. Now this theory has become full- fledged research area lying at the intersection of nonlinear analysis and probability theory. In this monograpgh those aspects of random solution of random operator equations and random operator inclusion, which fall within the scope of investigation of random fixed point are discussed.

Download or read book Spectral Theory of Random Schr dinger Operators written by R. Carmona and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Random Schr dinger Operators written by Margherita Disertori and published by SMF. This book was released on 2008 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last thirty years, random Schrodinger operators, which originated in condensed matter physics, have been studied intensively and very productively. The theory is at the crossroads of a number of mathematical fields: the theory of operators, partial differential equations, the theory of probabilities, in particular the study of stochastic processes and that of random walks and Brownian motion in a random environment. This monograph aims to give the reader a panorama of the subject, from the now-classic foundations to very recent developments.

Download or read book Operator Theory with a Random Potential and Some Questions of Statistical Physics written by Viktor Nikolaevich Popov and published by American Mathematical Soc.. This book was released on 1991 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Spectral Theory of Random Schr dinger Operators written by Reinhard Lang and published by Springer. This book was released on 2006-11-14 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.

Download or read book Spectral Theory of Random Schrodinger Operators written by R. Carmona and published by . This book was released on 1990-01-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Existence and Regularity Properties of the Integrated Density of States of Random Schr dinger Operators written by Ivan Veselic and published by Springer Science & Business Media. This book was released on 2008-01-02 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.

Download or read book Spectral Theory of Random Schrodinger Operators written by Reinhard Lang and published by . This book was released on 2014-01-15 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Random Linear Operators written by A.V. Skorohod and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Random Integral Equations written by Bharucha-Reid and published by Academic Press. This book was released on 1973-03-02 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Integral Equations

Download or read book Spectra of Random and Almost Periodic Operators written by Leonid Pastur and published by Springer. This book was released on 2011-12-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Products of Random Matrices with Applications to Schr dinger Operators written by P. Bougerol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fredholm Theory with Applications to Random Operators written by and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the Fredholm theory of bounded linear operators acting on Banach space valued sequence spaces. As an application, random operators are considered and studied in detail. One of the most important tools in the study of operators on sequence spaces is the concept of limit operators. The correspondence between an operator and its limit operators is studied regarding properties like spectrum, pseudospectrum and numerical range. It turns out that similar theorems can be formulated for all these properties, respectively. These results prove to be particularly useful in the case of random operators. Special attention is directed to the so-called Feinberg-Zee random hopping matrix, which, despite its simple appearance, seems to have a very complicated spectrum. With the help of new methods, improved upper and lower bounds to the spectrum are obtained. One of these lower bounds is an infinite sequence of Julia sets, which emphasizes the complexity of the spectrum of this particular operator.$cen$dAbstract

Download or read book Spectral Theory of Schrodinger Operators written by Rafael del Río and published by American Mathematical Soc.. This book was released on 2004 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.

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.