Article
Comm. Math. Phys.
Probabilistic averages of Jacobi operators
Helge Krüger
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.
I use this to show that for finite gap Jacobi operators, regularity
implies that they are in the Ces\`aro-Nevai class, proving a conjecture
of Barry Simon. Furthermore, I use this to study Jacobi operators
with coefficients a(n) = 1 and b(n) = f(n\rho \pmod{1}) for
\rho > 0 not an integer.
MSC2000: Primary 81Q10; Secondary 37D25, 47B36
Keywords: Lyapunov Exponents, Schrodinger Operators, Ergodic Decomposition