University of Toronto
                  PDE/Applied Math/Analysis Seminar
                Friday 15. February 2008, 1:10-2:00pm
                          6183 Bahen Center      



SPEAKER:  Eugene Kritchevski, McGill University

TITLE:    Poisson statistics of eigenvalues for random 
          discrete Schrodinger operators.

ABSTRACT: In this talk, I will consider random discrete 
          Schrodinger operators of the form H= L+ c V acting on 
          the Hilbert space l^2(X), where X is a given countable 
          set endowed with a nice homogeneous structure: e.g. the 
          lattice Z^d, a regular  tree, or a hierarchical lattice. 
          Here L is a given self-adjoint operator on l^2(X) e.g. 
          the discrete or the hierarchical Laplacian,  V is a 
          random potential (Vf)(x)=v(x)f(x) with v(x) i.i.d. 
          random variables, and c>0 is a coupling constant 
          measuring the strength of the disorder. 

          One is interested to understand the statistical behavior 
          of the random eigenvalues of large finite volume 
          approximations to H in the thermodynamic limit. In some 
          cases it is possible to prove that, after a natural 
          rescaling, the random eigenvalues behave as a Poisson 
          point process.  After reviewing the known results for 
          the Anderson model on Z^d and for the regular tree, I will 
          discuss my work on the hierarchical model. I will explain 
          the mechanism responsible for Poisson statistics of 
          eigenvalues and, if time permits, results on generic 
          spectral localization.  


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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2007-2008 organizers:
          Walid Abou-Salem      walid@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
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