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＜電子ブック＞
Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators / by Ivan Veselic
(Lecture Notes in Mathematics. ISSN:16179692 ; 1917)

版	1st ed. 2008.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	X, 147 p : online resource
著者標目	*Veselic, Ivan author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Differential equations LCSH:Dynamical systems FREE:Probability Theory FREE:Differential Equations FREE:Dynamical Systems
一般注記	Random Operators -- Existence of the Integrated Density of States -- Wegner Estimate -- Wegner’s Original Idea. Rigorous Implementation -- Lipschitz Continuity of the IDS The theory of random Schrödinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids. Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods. The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function. Various approaches to the construction of the integrated density of states and the proof of its regularity properties are presented. The setting is general enough to apply to random operators on Riemannian manifolds with a discrete group action. References to and a discussion of other properties of the IDS are included, as are a variety of models beyond those treated in detail here HTTP:URL=https://doi.org/10.1007/978-3-540-72691-3

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