caa a22 4500 445836075 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0647-z doi (NATIONALLICENCE)springer-10.1007/s00209-009-0647-z Tanaka Ryokichi Department of Mathematics, Kyoto University, 606-8502, Kyoto, Japan aut Large deviation on a covering graph with group of polynomial growth [Elektronische Daten] [Ryokichi Tanaka] 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. Springer-Verlag, 2009 Large deviations nationallicence Random walk nationallicence Nilpotent group nationallicence Carnot-Carathéodory metric nationallicence Gromov-Hausdorff convergence nationallicence Discrete geometry nationallicence Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 803-833 0025-5874 267:3-4<803 2011 267 209 https://doi.org/10.1007/s00209-009-0647-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0647-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tanaka Ryokichi Department of Mathematics, Kyoto University, 606-8502, Kyoto, Japan aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 803-833 0025-5874 267:3-4<803 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer