ID | 53045 |
FullText URL | |
Author |
Ishiwata, Satoshi
Teruya, Tsubasa
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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.
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Keywords | Non-symmetric random walk
asymptotic expansion
triangular lattice
standard realization
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Published Date | 2015-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume57
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 129
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End Page | 148
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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Copyright Holders | Copyright©2015 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol57/iss1/8
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JaLCDOI |