Random Operator Theory

Author : Reza Saadati
Publisher : Academic Press
Page : 82 pages
File Size : 53,8 Mb
Release : 2016-08-24
Category : Mathematics
ISBN : 9780081009550

Get Book

Random Operator Theory by Reza Saadati Pdf

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

Author : Michael Aizenman,Simone Warzel
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 40,9 Mb
Release : 2015-12-11
Category : Functional analysis -- Miscellaneous applications of functional analysis -- Applications in quantum physics
ISBN : 9781470419134

Get Book

Random Operators by Michael Aizenman,Simone Warzel Pdf

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.

Author : R. Carmona,J. Lacroix
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461244882

Get Book

Spectral Theory of Random Schrödinger Operators by R. Carmona,J. Lacroix Pdf

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.

Author : Margherita Disertori,Werner Kirsch,Abel Klein
Publisher : SMF
Page : 244 pages
File Size : 42,6 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015072684635

Get Book

Random Schrödinger Operators by Margherita Disertori,Werner Kirsch,Abel Klein Pdf

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.

Author : Bharucha-Reid
Publisher : Academic Press
Page : 266 pages
File Size : 52,8 Mb
Release : 1973-03-02
Category : Computers
ISBN : 9780080956053

Get Book

Random Integral Equations by Bharucha-Reid Pdf

Random Integral Equations

Author : A.V. Skorohod
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 52,7 Mb
Release : 2001-11-30
Category : Mathematics
ISBN : 1402003269

Get Book

Random Linear Operators by A.V. Skorohod Pdf

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.

Author : Leonid Andreevich Pastur,Mariya Shcherbina
Publisher : American Mathematical Soc.
Page : 650 pages
File Size : 52,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852859

Get Book

Eigenvalue Distribution of Large Random Matrices by Leonid Andreevich Pastur,Mariya Shcherbina Pdf

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.

Author : Viktor Nikolaevich Popov
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 52,5 Mb
Release : 1991
Category : Mathematics
ISBN : 0821831399

Get Book

Operator Theory with a Random Potential, and Some Questions of Statistical Physics by Viktor Nikolaevich Popov Pdf

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.

Author : Reinhard Lang
Publisher : Unknown
Page : 136 pages
File Size : 46,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662191512

Get Book

Spectral Theory of Random Schrodinger Operators by Reinhard Lang Pdf

Author : Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland
Publisher : Birkhäuser
Page : 313 pages
File Size : 54,5 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9783319470795

Get Book

Recent Trends in Operator Theory and Partial Differential Equations by Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland Pdf

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.

Author : Shih-sen Chang,Yeol Je Cho,Sin-min Kang
Publisher : Nova Publishers
Page : 358 pages
File Size : 53,9 Mb
Release : 2001
Category : Mathematics
ISBN : 1560729805

Get Book

Nonlinear Operator Theory in Probablistic Metric Spaces by Shih-sen Chang,Yeol Je Cho,Sin-min Kang Pdf

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.

Author : Reinhard Lang
Publisher : Springer
Page : 133 pages
File Size : 53,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540466277

Get Book

Spectral Theory of Random Schrödinger Operators by Reinhard Lang Pdf

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.

Author : Thomas L. Saaty
Publisher : RWS Publications
Page : 490 pages
File Size : 55,7 Mb
Release : 2014-12-22
Category : Business & Economics
ISBN : 9781888603392

Get Book

Non Linear Mathematics Vol. II by Thomas L. Saaty Pdf

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.

Author : Ivan Veselic
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 47,8 Mb
Release : 2008-01-02
Category : Mathematics
ISBN : 9783540726890

Get Book

Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators by Ivan Veselic Pdf

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.

Author : Vladimir Aleksandrovich Marchenko
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 41,9 Mb
Release : 1994
Category : Differential operators
ISBN : 082184122X

Get Book

Spectral Operator Theory and Related Topics by Vladimir Aleksandrovich Marchenko Pdf

"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.