5 research outputs found
Modification of polyolefins and polyvinylchloride by the radiation-induced graft polymerization
Longitudinal statistics of plasma bubbles observed as He+ density depletions at altitudes of the topside ionosphere
Eigenvalue Order Statistics for Random Schrödinger Operators with Doubly-Exponential Tails
We consider random Schrödinger operators of the form , where is the lattice Laplacian on and is an i.i.d. random field, and study the extreme order statistics of the Dirichlet eigenvalues for this operator restricted to large but finite subsets of . We show that, for with a doubly-exponential type of upper tail, the upper extreme order statistics of the eigenvalues falls into the Gumbel max-order class, and the corresponding eigenfunctions are exponentially localized in regions where takes large, and properly arranged, values. The picture we prove is thus closely connected with the phenomenon of Anderson localization at the spectral edge. Notwithstanding, our approach is largely independent of existing methods for proofs of Anderson localization and it is based on studying individual eigenvalue/eigenfunction pairs and characterizing the regions where the leading eigenfunctions put most of their mass