Large deviation on a covering graph with group of polynomial growth

Ryokichi Tanaka

doi:10.1007/s00209-009-0647-z

Large deviation on a covering graph with group of polynomial growth

Ryokichi Tanaka

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We discuss a large deviation principle of a periodic random walk on a covering graph with its transformation group of polynomial volume growth in view of geometry. As we shall observe, the behavior of a random walk at infinity is closely related to the Gromov-Hausdorff limit of an infinite graph and in the case where the graph admits an action of a group of polynomial volume growth, the Carnot-Carathéodory metric shows up in its limit space.

Original language	English
Pages (from-to)	803-833
Number of pages	31
Journal	Mathematische Zeitschrift
Volume	267
Issue number	3
DOIs	https://doi.org/10.1007/s00209-009-0647-z
Publication status	Published - 2011 Apr 1
Externally published	Yes

Keywords

Carnot-Carathéodory metric
Discrete geometry
Gromov-Hausdorff convergence
Large deviations
Nilpotent group
Random walk

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-009-0647-z

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AB - We discuss a large deviation principle of a periodic random walk on a covering graph with its transformation group of polynomial volume growth in view of geometry. As we shall observe, the behavior of a random walk at infinity is closely related to the Gromov-Hausdorff limit of an infinite graph and in the case where the graph admits an action of a group of polynomial volume growth, the Carnot-Carathéodory metric shows up in its limit space.

KW - Carnot-Carathéodory metric

KW - Discrete geometry

KW - Gromov-Hausdorff convergence

KW - Large deviations

KW - Nilpotent group

KW - Random walk

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Large deviation on a covering graph with group of polynomial growth

Abstract

Keywords

ASJC Scopus subject areas

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