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 −Δ +  γV , where the potentials , are i.i.d.  nonnegative random variables and γ > 0 is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like as γ tends to 0. Here the constant c is the s...

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Bibliographic Details
Published in:Probability theory and related fields 2011-06, Vol.150 (1-2), p.43-59
Main Authors: Kosygina, Elena, Mountford, Thomas S., Zerner, Martin P. W.
Format: Article
Language:English
Subjects:
Annealing
Chaos theory
Economics
Exact sciences and technology
Finance
General topics
Green's functions
Insurance
Liapunov exponents
Lyapunov exponents
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probabilistic methods
Probability
Probability and statistics
Probability theory
Probability Theory and Stochastic Processes
Quantitative Finance
Quenching
Quenching (cooling)
Random variables
Random walk theory
Scalars
Sciences and techniques of general use
Statistics for Business
Stochastic processes
Studies
Theoretical
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Summary:We consider quenched and annealed Lyapunov exponents for the Green’s function of −Δ +  γV , where the potentials , are i.i.d.  nonnegative random variables and γ > 0 is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like as γ 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.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-010-0266-y