On the Sum of the Non-Negative Lyapunov Exponents for Some Cocycles Related to the Anderson Model

Abstract

We provide an explicit lower bound for the the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model. In particular, for the Anderson model on a strip of width $W$ the lower bound is proportional to $W^{-\epsilon }$, for any $\epsilon >0$. This bound is consistent with the fact that the lowest non-negative Lyapunov exponent is conjectured to have a lower bound proportional to $W^{-1}$.

References in corpus (3)

• Eigenvector localization for random band matrices with power law band width
• Generalized eigenvalue-counting estimates for the Anderson model
• A lower bound for the Lyapounov exponents of the random Schrodinger operator on a strip