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タイトル:Long-time asymptotics of random walks on covering graphs with groups of polynomial volume growth
講演者:難波 隆弥(立命館大学)
アブストラクト:
日時:2021年4月23日(金) 16:30~18:00
タイトル:Long-time asymptotics of random walks on covering graphs with groups of polynomial volume growth
講演者:難波 隆弥(立命館大学)
アブストラクト:
We discuss central limit theorems (CLTs) for non-symmetric random walks on covering graphs of finite graphs whose covering transformation groups are groups of polynomial volume growth. By realizing the covering graph into a certain nilpotent Lie group through a discrete harmonic map, we show that the limiting semigroup is generated by the sub-Laplacian with a non-trivial linear drift on the nilpotent Lie group equipped with the Albanese metric. Furthermore, under the centered condition, we establish a functional CLT (i.e., Donsker-type invariance principle) in a Hölder space over the nilpotent Lie group by employing the theory of rough paths. As a refinement of the CLT, we also establish the Edgeworth expansion of the random walk even if the random walk is non-symmetric. A part of this talk is based on joint work with Satoshi Ishiwata (Yamagata) and Hiroshi Kawabi (Keio).
開催方法:Zoom配信での開催です.
問い合わせ先:立命館大学理工学部数理科学科 多羅間 大輔