171390
20181203022532.0
10.1007/s00440-010-0266-y
doi
000290725200002
ISI
ARTICLE
Lyapunov exponents of Green's functions for random potentials tending to zero
2011
2011
Journal Articles
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.
Annealed
Green's function
Lyapunov exponent
Quenched
Random potential
Random walk
Random-Walks
Bounds
Z(D)
Kosygina, Elena
Baruch Coll, Dept Math, New York, NY 10010 USA
Mountford, Thomas S.
Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne, Switzerland
138859
244703
Zerner, Martin P. W.
Univ Tubingen, Math Inst, D-72076 Tubingen, Germany
43-59
Probability Theory And Related Fields
150
PRST
252347
U10128
oai:infoscience.tind.io:171390
article
SB
EPFL-ARTICLE-171390
EPFL
PUBLISHED
REVIEWED
ARTICLE