Probabilistic averages of Jacobi operators

Details Probabilistic averages of Jacobi operators Probabilistic averages of Jacobi operators

2009-04-27

arxiv.org/abs/0904.4226v1

Mathematics

Spectral Theory

Scientific paper

I study the Lyapunov exponent and the integrated density of states for
general Jacobi operators. The main result is that questions about these, can be
reduced to questions about ergodic Jacobi operators. Then, I apply this to
$a(n) = 1$ and $b(n) = f(n^\rho \pmod{1})$ for $\rho > 0$ not an integer, and
to obtain a probabilistic version of the Denisov--Rakhmanov--Remling Theorem.

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