Probability Seminar: Christian Sadel

  • Date: 09/18/2013
  • Time: 15:00
Christian Sadel (UBC)

University of British Columbia


Limit stochastic differential equations (SDEs) for products of random matrices


We consider the Markov process given by products of i.i.d. random matrices that are perturbations of a fixed non-random matrix and the randomness is coupled with some small coupling constant. Such random products occur in terms of transfer matrices for random quasi-one dimensional Schrodinger operators with i.i.d. matrix potential. Letting the number of factors going to infi nity and the random disorder going to zero in a critical scaling we obtain a limit process for a certain Schur complement of the random products. This limit is described by an SDE. This allows us to obtain a limit SDE for the Markov processes given by the action of the random products on Grassmann and flag manifolds. Applied to random quasi-one dimensional Schrodinger operators we can describe the limiting eigenvalue process in a critical scaling by the zero process of a determinant of a matrix-valued function described by an SDE.
Joint work with B. Virag.

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Location: ESB 2012