The relation between quenched and annealed Lyapunov exponents in random potential on trees |
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Authors: | Gundelinde Maria Wiegel |
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Institution: | Graz University of Technology, Austria |
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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. |
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Keywords: | 60K37 05C05 Random walks Random potential Lyapunov exponents Homogeneous trees Relative entropy |
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