Kosygina, Elena
Mountford, Thomas S.
Zerner, Martin P. W.
Lyapunov exponents of Green's functions for random potentials tending to zero
Probability Theory And Related Fields
Probability Theory And Related Fields
Probability Theory And Related Fields
Probability Theory And Related Fields
150
Annealed
Green's function
Lyapunov exponent
Quenched
Random potential
Random walk
Random-Walks
Bounds
Z(D)
2011
2011
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.
Probability Theory And Related Fields
Journal Articles
10.1007/s00440-010-0266-y