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research article
Lyapunov exponents of Green's functions for random potentials tending to zero
We consider quenched and annealed Lyapunov exponents for the Green's function of -Delta + gamma V, where the potentials V(x) ,x epsilon Z(d), are i.i.d. nonnegative random variables and gamma > 0 is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like root gamma as gamma tends to 0. Here the constant c is the same for the quenched as for the annealed exponent and is computed explicitly. This improves results obtained previously by Wang. We also consider other ways to send the potential to zero than multiplying it by a small number.
Type
research article
Web of Science ID
WOS:000290725200002
Authors
Publication date
2011
Published in
Volume
150
Start page
43
End page
59
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
December 16, 2011
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