Dynamical Localization for Random Band Matrices up to W≪N^{1/4}

Dynamical Localization for Random Band Matrices up to W≪N^{1/4}

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Jacob Shapiro, Princeton University
Fine Hall 314

Random band matrices provide a simple model for studying the metal-insulator transition of the Anderson model. After giving some background on this problem I will present a recent simple proof that N×N Gaussian random band matrices with band width W exhibit dynamical Anderson localization at all energies when WN^{1/4}. The proof uses the fractional moment method and an adaptive Mermin-Wagner style shift. Joint with Cipolloni, Peled, and Schenker.