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arXiv · 2011.13783

Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth

Ryuya Namba
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Abstract

Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the underlying graphs but also the modified harmonic embedding of the graph into a certain nilpotent Lie group. Moreover, we apply the rate of convergence in Trotter's approximation theorem to establish the Berry-Esseen type bound for the random walks.

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Ryuya Namba. 2020-11-27. Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth. https://doi.org/10.1007/s10959-021-01111-7

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