Central limit theorems for biased randomly trapped random walks on Z

Adam Bowditch

Stochastic Processes and their Applications, 2019, vol. 129, issue 3, 740-770

Abstract: We prove CLTs for biased randomly trapped random walks in one dimension. By considering a sequence of regeneration times, we will establish an annealed invariance principle under a second moment condition on the trapping times. In the quenched setting, an environment dependent centring is necessary to achieve a central limit theorem. We determine a suitable expression for this centring. As our main motivation, we apply these results to biased walks on subcritical Galton–Watson trees conditioned to survive for a range of bias values.

Keywords: Random walk; Random environment; Randomly trapped; Galton–Watson tree; Annealed; Quenched; Functional central limit theorem; Invariance principle (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.03.017

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