Renormalization of Random Jacobi Operators

  title={Renormalization of Random Jacobi Operators},
  author={Oliver Knill},
We construct a Cantor set ̂ of limit-periodic Jacobi operators having the spectrum on the Julia set J of the quadratic map z ι-> z + E for large negative real numbers E. The density of states of each of these operators is equal to the unique equilibrium measure μ on J. The Jacobi operators in $ are defined over the von Neumann-Kakutani system, a group translation on the compact topological group of dyadic integers. The Cantor set $ is an attractor of the iterated function system built up by the… CONTINUE READING
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