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Large Deviations for Radial Random Walks on Homogeneous Trees

Published online by Cambridge University Press:  11 January 2016

Kanji Ichihara
Kanji Ichihara*
Affiliation:
Department of Mathematics, Faculty of Engineering Science, Kansai University, Suita, Osaka 564-8680, Japan, kchihara@ipcku.kansai-u.ac.jp
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Abstract

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Donsker-Varadhan’s type large deviation will be discussed for the pinned motion of a radial random walk on a homogeneous tree. We shall prove that the rate function corresponding to the large deviation is associated with a new Markov chain constructed from the above random walk through a harmonic transform based on a positive principal eigenfunction for the generator of the random walk.

Keywords

60F1060J10

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 187 , September 2007, pp. 75 - 90
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[1] Chiyonobu, T., Ichihara, K. and Mituisi, H., Large Deviation for Periodic Markov Process on Square Lattice, J. Math. Sci. Univ. Tokyo, 13 (2006), 525–544.Google Scholar
[2] Donsker, M. D. and Varadhan, S. R. S., Asymptotic evaluation of certain Markov process expectations for large time, I, Comm. Pure Appl. Math., 28 (1975), 1–47.CrossRefGoogle Scholar
[3] Donsker, M. D. and Varadhan, S. R. S., Asymptotic evaluation of certain Markov process expectations for large time, III, Comm. Pure Appl. Math., 29 (1976), 389–461.CrossRefGoogle Scholar
[4] Figà-Talamanca, A. and Nebbia, C., Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees, London Mathematical Society Lecture Note Series, vol. 162.Google Scholar
[5] Ichihara, K., Large deviation for pinned covering diffusion, Bull. Sci. math., 125 (2001), 529–551.CrossRefGoogle Scholar
[6] Lalley, S., Finite range random walks on free groups and homogeneous trees, Ann. Prob., 21 (1993), 2087–2130.CrossRefGoogle Scholar
[7] Ledrappier, F., Some asymptotic properties of random walks on free groups, Topics in probability and Lie groups: boundary theory, CRM Proc. Lecture Notes, vol. 28, Amer. Math. Soc., Providence, RI, 2001, pp. 117–152.CrossRefGoogle Scholar
[8] Sawyer, S., Isotropic random walks in a tree, Zeit. Wahr. verw. Gebiete, 42 (1978), 279–292.CrossRefGoogle Scholar
[9] Sawyer, S. and Steger, T., The rate of escape for anisotropic random walks in a tree, Prob. Th. Rel. Fields, 76 (1987), 207–230.CrossRefGoogle Scholar
[10] Woess, W., Random walks on infinite graphs and groups, Cambridge Tracts in Mathematics, vol. 138, Cambridge University Press.Google Scholar