Quebec Mathematical Sciences Colloquium

October 6, 2006 from 16:00 to 18:00 (Montreal/Miami time) On location

Randomness, and its effects on Spectra

Colloquium presented by Michael Aizenman (Princeton University)

Randomness is a known source of deterministic laws. A manifestation of that is found in the spectral theory of linear operators which incorporate extensive disorder. Among the relevant issues is the distinction between regimes of pure-point and of continuous spectra, and in the finite-volume case questions concerning the local level statistics. Observations made in different contexts have led to the somewhat vaguely expressed expectation that the distribution of the level statistics in regimes of continuous spectrum generically resembles the distribution found in the Wigner random matrix ensembles. A different law, the Poisson distribution, is known to describe the level statistics in regimes of spectral localization. We shall comment on interesting deviations from this dichotomy, and also outline some recent works concerning related topics in the context of Schroedinger operators with random potential, and random quantum graph operators.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., Salle / Room SH-3420