Dear colleagues, I would like to invite you to the following online seminar organized by the Probability group of the University of Pisa. The talk will be accessible under the link Click here to join<https://teams.microsoft.com/l/meetup-join/19:af3d635091e049579e555a84219ab378@thread.tacv2/1619032463032?context={"Tid":"c7456b31-a220-47f5-be52-473828670aa1","Oid":"dfd1e5f6-331d-43e0-a180-4bb6ce727fb7"}> Best regards, Giacomo Tuesday, April 27, 16:00 Speaker: Constanza Rojas-Molina (CY Cergy Paris Université) Title: (Fractional) random Schrödinger operators, integrated density of states and localization Abstract: We consider the continuous Schrödinger operator - d^2/d^x^2 + B’(x) on the interval [0,L] where the potential B’ is a white noise. We study the entire spectrum of this operator in the large L limit. We prove the joint convergence of the eigenvalues and of the eigenvectors and describe the limiting shape of the eigenvectors for all energies. When the energy is much smaller than L, we find that we are in the localized phase and the eigenvalues are distributed as a Poisson point process. The transition towards delocalization holds for large eigenvalues of order L. In this regime, we show the convergence at the level of operators. The limiting operator in the delocalized phase is acting on R^2-valued functions and is of the form ``J \partial_t + 2*2 noise matrix'' (where J is the matrix ((0, -1)(1, 0))), a form appearing as a conjecture by Edelman Sutton (2006) for limiting random matrices. Joint works with Cyril Labbé. ************************ Giacomo Di Gesù Dipartimento di Matematica Università di Pisa Largo Bruno Pontecorvo 5 56127 - Pisa, Italy giacomo.digesu@unipi.it<mailto:giacomo.digesu@unipi.it> https://sites.google.com/site/giacomodigesu/