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SUMMARY:Laure Dumaz (École Normale supérieure)
DTSTART:20210413T140000Z
DTEND:20210413T150000Z
DTSTAMP:20260423T052805Z
UID:POSemP/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POSemP/1/">L
 ocalization of the continuous Anderson hamiltonian in 1-d and its transiti
 on towards delocalization</a>\nby Laure Dumaz (École Normale supérieure)
  as part of Pisa Online Seminar in Probability\n\n\nAbstract\nWe 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 spe
 ctrum of this operator in the large L limit. We prove the joint convergenc
 e of the eigenvalues and of the eigenvectors and describe the limiting sha
 pe of the eigenvectors for all energies. When the energy is much smaller t
 han L\, we find that we are in the localized phase and the eigenvalues are
  distributed as a Poisson point process. The transition towards delocaliza
 tion holds for large eigenvalues of order L. In this regime\, we show the 
 convergence at the level of operators. The limiting operator in the deloca
 lized phase is acting on R^2-valued functions and is of the form ``J \\par
 tial_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 rando
 m matrices. Joint works with Cyril Labbé.\n
LOCATION:https://researchseminars.org/talk/POSemP/1/
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