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Random Schrödinger operator on fractals

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FDE2 - Fractional differential equations

                                  Random Schrödinger operator on fractals                 Stanislav Molchanov (UNC Charlotte, USA ; HSE, Moscow, Russia)   The talk will discuss two groups of localization theorems. The first one concerns the Anderson model for graphs similar to the Sierpinski lattice. The spectral dimension of each graph is less than 2 and – in the spirit of the classical conjecture – in the wide class of random potentials, the spectrum is pure point for an arbitrary small disorder. The theorems of the second group present localization results for continuous hierarchical Schrödinger operators. The central fact: for potentials of a certain class (finite rank random potentials), the spectrum is pure point in any dimension and arbitrary coupling constant.

This talk is part of the Isaac Newton Institute Seminar Series series.

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