2011/01/18 by Johannes Rueß, Rueß, Johannes · 1 citation
Mathematics · Physics and Astronomy · #60J65 (Primary) #60K37 #82B44 (Secondary) #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J65 #msc:60K37 #msc:82B44
paper · pdf · doi:10.48550/arxiv.1101.3404
Now 14 pages, 2 figures. Some references added, abstract changed, 2 new paragraphs in the introduction
openalex publication_date 2011/01/18 · arxiv created 2011/10/19 · arxiv updated 2011/10/20 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We investigate Lyapunov exponents of Brownian motion in a nonnegative Poissonian potential V. The Lyapunov exponent depends on the potential V and our interest lies in the decay rate of the Lyapunov exponent if the potential V tends to zero. In our model the random potential V is generated by locating at each point of a Poisson point process with intensity ν a bounded compactly supported nonnegative function W. We show that for sequences of potentials Vn for which νn ‖Wn‖1 ∼ D/n for some constant D > 0 (n → ∞), the decay rates to zero of the quenched and annealed Lyapunov exponents coincide and equal c n-1/2 where the constant c is computed explicitly. Further we are able to estimate the quenched Lyapunov exponent norm from above by the corresponding norm for the averaged potential.