Singular components of spectral measures for ergodic Jacobi matrices

Details Singular components of spectral measures for ergodic Jacobi matrices Singular components of spectral measures for ergodic Jacobi matrices

2011-04-18

arxiv.org/abs/1104.3376v2

Journal of Mathematical Physics 52 (2011), 073508

Mathematics

Spectral Theory

to appear in the Journal of Mathematical Physics, vol 52 (2011)

Scientific paper

For ergodic 1d Jacobi operators we prove that the random singular components
of any spectral measure are almost surely mutually disjoint as long as one
restricts to the set of positive Lyapunov exponent. In the context of extended
Harper's equation this yields the first rigorous proof of the Thouless' formula
for the Lyapunov exponent in the dual regions.

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