Spectral Theory of Random Schr�dinger Operators: A Genetic Introduction (Lecture Notes in Mathematics, 1498)

Lang, Reinhard

ISBN 10: 3540549757 ISBN 13: 9783540549758

Editorial: Springer, 1991

Idioma: Ingl�s

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T�tulo

Spectral Theory of Random Schr�dinger Operators: A Genetic Introduction (Lecture Notes in Mathematics, 1498)

Editor

Springer

Fecha de publicaci�n

1991

Idioma

Ingl�s

ISBN 10

3540549757

ISBN 13

9783540549758

Encuadernaci�n

Encuadernaci�n de tapa blanda

Estado

New

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Sinopsis

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.

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