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SUMMARY:Constanza Rojas-Molina (CY Cergy Paris Université)
DTSTART:20210427T140000Z
DTEND:20210427T150000Z
DTSTAMP:20260423T052709Z
UID:POSemP/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POSemP/3/">(
 Fractional) random Schrödinger operators\, integrated density of states a
 nd localization</a>\nby Constanza Rojas-Molina (CY Cergy Paris Université
 ) as part of Pisa Online Seminar in Probability\n\n\nAbstract\nIn this tal
 k we will review some recent results on random Schrödinger operators\, wh
 ich are used to model electronic transport in disordered quantum systems a
 nd to study the phenomenon of Anderson localization. After a short introdu
 ction to the subject\, we will focus on a particular type of random operat
 or driven by a fractional laplacian. The interest on the latter lies in th
 eir association to stable Levy processes\, random walks with long jumps an
 d anomalous diffusion. We will discuss in this talk the interplay between 
 the non-locality of the fractional laplacian and the localization properti
 es of the random potential in the fractional Anderson model\, in both the 
 continuous and discrete settings. In the discrete setting we study the int
 egrated density of states and show a fractional version of Lifshitz tails.
  This coincides with results obtained in the continuous setting by the pro
 bability community. This is based on joint work with M. Gebert (LMU Munich
 ).\n
LOCATION:https://researchseminars.org/talk/POSemP/3/
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