Edgeworth Expansions for Centered Random Walks on Covering Graphs of Polynomial Volume Growth
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...
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| Veröffentlicht in: | Journal of theoretical probability 2022-09, Vol.35 (3), p.1898-1938 |
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| container_end_page | 1938 |
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| container_issue | 3 |
| container_start_page | 1898 |
| container_title | Journal of theoretical probability |
| container_volume | 35 |
| creator | Namba, Ryuya |
| description | 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. |
| doi_str_mv | 10.1007/s10959-021-01111-7 |
| format | Article |
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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. 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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.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10959-021-01111-7</doi><tpages>41</tpages></addata></record> |
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| ispartof | Journal of theoretical probability, 2022-09, Vol.35 (3), p.1898-1938 |
| issn | 0894-9840 1572-9230 |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Graphs Lie groups Mathematics Mathematics and Statistics Polynomials Probability Theory and Stochastic Processes Random walk Statistics Thermal expansion |
| title | Edgeworth Expansions for Centered Random Walks on Covering Graphs of Polynomial Volume Growth |
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