Advertisement

Spectral Theory of Random Schrödinger Operators

A Genetic Introduction

  • Authors
  • Reinhard Lang
Conference proceedings

Part of the Lecture Notes in Mathematics book series (LNM, volume 1498)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Reinhard Lang
    Pages 1-5
  3. Reinhard Lang
    Pages 6-18
  4. Reinhard Lang
    Pages 19-29
  5. Reinhard Lang
    Pages 30-42
  6. Reinhard Lang
    Pages 113-118
  7. Back Matter
    Pages 119-125

About these proceedings

Introduction

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.

Keywords

Brownian motion Entropy Large Deviations Potential Random Schroedinger Operators Spectral Theory Stochastic Analysis

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093929
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54975-8
  • Online ISBN 978-3-540-46627-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
Industry Sectors
Pharma
Biotechnology
Finance, Business & Banking
IT & Software
Telecommunications
Consumer Packaged Goods
Aerospace
Oil, Gas & Geosciences
Engineering