On the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model
Copyright policy )On the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model
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 $W^{-1}$.
- University of Toronto Canada
cocycles, 82B44 (Primary), 47B36 (Secondary), 81Q10, Lyapunov exponents, Random operators and equations (aspects of stochastic analysis), FOS: Physical sciences, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Mathematics - Spectral Theory, FOS: Mathematics, Mathematics - Dynamical Systems, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Spectral Theory (math.SP), Mathematical Physics, Anderson model
cocycles, 82B44 (Primary), 47B36 (Secondary), 81Q10, Lyapunov exponents, Random operators and equations (aspects of stochastic analysis), FOS: Physical sciences, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Mathematics - Spectral Theory, FOS: Mathematics, Mathematics - Dynamical Systems, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Spectral Theory (math.SP), Mathematical Physics, Anderson model
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