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ID 53045
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Author
Ishiwata, Satoshi
Teruya, Tsubasa
Abstract
In the present paper, we study an explicit effect of non-symmetry on asymptotics of the n-step transition probability as n → ∞ for a class of non-symmetric random walks on the triangular lattice. Realizing the triangular lattice into R2 appropriately, we observe that the Euclidean distance in R2 naturally appears in the asymptotics. We characterize this realization from a geometric view point of Kotani-Sunada’s standard realization of crystal lattices. As a corollary of the main theorem, we obtain that the transition semigroup generated by the non-symmetric random walk approximates the heat semigroup generated by the usual Brownian motion on R2.
Keywords
Non-symmetric random walk
asymptotic expansion
triangular lattice
standard realization
Published Date
2015-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume57
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
129
End Page
148
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2015 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol57/iss1/8
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