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On the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model

Published online by Cambridge University Press:  06 October 2015

ILIA BINDER ,
MICHAEL GOLDSTEIN  and
MIRCEA VODA
ILIA BINDER
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada email ilia@math.utoronto.ca, gold@math.utoronto.ca, mvoda@math.utoronto.ca
MICHAEL GOLDSTEIN
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada email ilia@math.utoronto.ca, gold@math.utoronto.ca, mvoda@math.utoronto.ca
MIRCEA VODA
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada email ilia@math.utoronto.ca, gold@math.utoronto.ca, mvoda@math.utoronto.ca
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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 $W^{-\unicode[STIX]{x1D716}}$, for any $\unicode[STIX]{x1D716}>0$. This bound is consistent with the fact that the lowest non-negative Lyapunov exponent is conjectured to have a lower bound proportional to $W^{-1}$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 2 , April 2017 , pp. 369 - 388
Copyright
© Cambridge University Press, 2015 

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