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Non-Gaussian fluctuations of randomly trapped random walks
Published online by Cambridge University Press: 08 October 2021
Abstract
In this paper we consider the one-dimensional, biased, randomly trapped random walk with infinite-variance trapping times. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable Lévy process. As our main motivation, we apply subsequential versions of our results to biased walks on subcritical Galton–Watson trees conditioned to survive. This confirms the correct order of the fluctuations of the walk around its speed for values of the bias that yield a non-Gaussian regime.
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust
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