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On the Strong Recurrence of Recurrent RWRE

Name: On the Strong Recurrence of Recurrent RWRE
Creator: Kochler, Michael
Keywords: Probability (math.PR), FOS: Mathematics, 0101 mathematics, 01 natural sciences, Mathematics - Probability

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2012Embargo end date: 01 Jan 2012Publisher:arXiv

Authors: Kochler, Michael;

doi: 10.48550/arxiv.1211.4770

arXiv: http://arxiv.org/abs/1211.4770

On the Strong Recurrence of Recurrent RWRE

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Abstract

We consider a recurrent RWRE $(X_n)_{n \in \mathbb{N}_0}$ on $\mathbb{Z}$ and investigate the quenched return probabilities of the RWRE to the origin for which we state results on their decay in terms of summability. Additionally, we give some examples for recurrent RWRE with a multidimensional state space which give reason for the part "strong recurrence" in the title of this paper when we compare the behaviour of RWRE with the behaviour of the symmetric random walk on $\mathbb{Z}^d$.

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Keywords

Probability (math.PR), FOS: Mathematics, Mathematics - Probability

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