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Central limit theorems for biased randomly trapped random walks on Z

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  • Bowditch, Adam

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.

Suggested Citation

  • Bowditch, Adam, 2019. "Central limit theorems for biased randomly trapped random walks on Z," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 740-770.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:3:p:740-770
    DOI: 10.1016/j.spa.2018.03.017
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    References listed on IDEAS

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    1. Gantert, Nina & Müller, Sebastian & Popov, Serguei & Vachkovskaia, Marina, 2012. "Random walks on Galton–Watson trees with random conductances," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1652-1671.
    2. Černý, Jiří & Wassmer, Tobias, 2015. "Randomly trapped random walks on Zd," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1032-1057.
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