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Spectral Theory of Random Schrödinger Operators
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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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