Spectral Theory of Random Schrodinger Operators

The interplay between the spectral theory of Schr|dingeroperators and probabilistic considerations forms the maintheme of these notes, written for the non-specialist readerand intended to provide a brief and elementaryintroductionto this field. An attempt is made to show basic ideas instatu nascendi and to follow their evaluation from simplebeginnings through to more advanced results. The term"e;genetic"e; in the title refers to this proceedure. The authorconcentrates on 2 topics which, in the history of thesubject, have been of major conceptual importance - on theone hand the Laplacian is a random medium and the left endof its spectrum (leading to large deviation problems forBrownian motion and the link to thenotion of entropy) andon the other, Schr|dinger operators with general ergodicpotentials in one-dimensional space. Ideas and concepts areexplained in the simplest, possible setting and by means ofa few characteristic problems with heuristic argumentspreceding rigorous proofs.