Large deviation on a covering graph with group of polynomial growth

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3 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 languageEnglish
Pages (from-to)803-833
Number of pages31
JournalMathematische Zeitschrift
Volume267
Issue number3
DOIs
Publication statusPublished - 2011 Apr 1
Externally publishedYes

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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