Edgeworth Expansions for Centered Random Walks on Covering Graphs of Polynomial Volume Growth

Ryuya Namba ()
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Ryuya Namba: Ritsumeikan University

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1898-1938

Abstract: 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 depend 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.

Keywords: Berry–Esseen-type bound; Edgeworth expansion; Covering graph; Centered random walk; 60F05; 60J10; 22E25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01111-7

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