Svetlana Ya Jitomirskaya

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Although concrete operators with singular continuous spectrum have proliferated recently [7,11,13,17,34,35,37,39], we still don’t really understand much about singular continuous spectrum. In part, this is because it is normally defined by what it isn’t — neither pure point nor absolutely continuous. An important point of view, going back in part to Rodgers(More)
We consider polynomials on the unit circle defined by the recurrence relation Φk+1(z) = zΦk(z)− αkΦk(z) k ≥ 0, Φ0 = 1 For each n we take α0, α1, . . . , αn−2 to be independent identically distributed random variables uniformly distributed in a disk of radius r < 1 and αn−1 to be another random variable independent of the previous ones and distributed(More)
We examine various issues relevant to localization in the Anderson model. We show there is more to localization than exponentially localized states by presenting an example with such states but where 〈x(t)2〉/t2−δ is unbounded for any δ > 0. We show that the recently discovered instability of localization under rank one perturbations is only a weak(More)