Random Operator Theory
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Author |
: Reza Saadati |
Publisher |
: Academic Press |
Total Pages |
: 84 |
Release |
: 2016-08-24 |
ISBN-10 |
: 9780081009550 |
ISBN-13 |
: 0081009550 |
Rating |
: 4/5 (50 Downloads) |
Synopsis Random Operator Theory by : Reza Saadati
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 |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 343 |
Release |
: 2015-12-11 |
ISBN-10 |
: 9781470419134 |
ISBN-13 |
: 1470419130 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Random Operators by : Michael Aizenman
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 |
: Ismat Beg |
Publisher |
: LAP Lambert Academic Publishing |
Total Pages |
: 164 |
Release |
: 2011-02 |
ISBN-10 |
: 3844310134 |
ISBN-13 |
: 9783844310139 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Solution of Random Operator Equations and Inclusions by : Ismat Beg
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.
Author |
: R. Carmona |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 611 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461244882 |
ISBN-13 |
: 1461244889 |
Rating |
: 4/5 (82 Downloads) |
Synopsis Spectral Theory of Random Schrödinger Operators by : R. Carmona
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 |
Publisher |
: SMF |
Total Pages |
: 244 |
Release |
: 2008 |
ISBN-10 |
: UOM:39015072684635 |
ISBN-13 |
: |
Rating |
: 4/5 (35 Downloads) |
Synopsis Random Schrödinger Operators by : Margherita Disertori
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 |
: Viktor Nikolaevich Popov |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 278 |
Release |
: 1991 |
ISBN-10 |
: 0821831399 |
ISBN-13 |
: 9780821831397 |
Rating |
: 4/5 (99 Downloads) |
Synopsis Operator Theory with a Random Potential, and Some Questions of Statistical Physics by : Viktor Nikolaevich Popov
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 |
: R. Carmona |
Publisher |
: |
Total Pages |
: 620 |
Release |
: 1990-01-01 |
ISBN-10 |
: 1461244897 |
ISBN-13 |
: 9781461244899 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Spectral Theory of Random Schrodinger Operators by : R. Carmona
Author |
: Reinhard Lang |
Publisher |
: Springer |
Total Pages |
: 133 |
Release |
: 2006-11-14 |
ISBN-10 |
: 9783540466277 |
ISBN-13 |
: 3540466274 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Spectral Theory of Random Schrödinger Operators by : Reinhard Lang
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 |
: Ivan Veselic |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 151 |
Release |
: 2008-01-02 |
ISBN-10 |
: 9783540726890 |
ISBN-13 |
: 3540726896 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators by : Ivan Veselic
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 |
: Reinhard Lang |
Publisher |
: |
Total Pages |
: 136 |
Release |
: 2014-01-15 |
ISBN-10 |
: 3662191512 |
ISBN-13 |
: 9783662191514 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Spectral Theory of Random Schrodinger Operators by : Reinhard Lang