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The relation between quenched and annealed Lyapunov exponents in random potential on trees

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  • Wiegel, Gundelinde Maria

Abstract

Our subject of interest is a simple symmetric random walk on the integers which faces a random risk to be killed. This risk is described by random potentials, which are defined by a sequence of independent and identically distributed non-negative random variables. To determine the risk of taking a walk in these potentials we consider the decay of the Green function. There are two possible tools to describe this decay: The quenched Lyapunov exponent and the annealed Lyapunov exponent. It turns out that on the integers and on regular trees we can state a precise relation between these two.

Suggested Citation

  • Wiegel, Gundelinde Maria, 2018. "The relation between quenched and annealed Lyapunov exponents in random potential on trees," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1988-2006.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:6:p:1988-2006
    DOI: 10.1016/j.spa.2017.08.020
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    References listed on IDEAS

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    1. Flury, Markus, 2007. "Large deviations and phase transition for random walks in random nonnegative potentials," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 596-612, May.
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