start-ver=1.4
cd-journal=joma
no-vol=57
cd-vols=
no-issue=1
article-no=
start-page=129
end-page=148
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2015
dt-pub=201501
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=AN EXPLICIT EFFECT OF NON-SYMMETRY OF RANDOM WALKS ON THE TRIANGULAR LATTICE
en-subtitle=
kn-subtitle=
en-abstract=
kn-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 R<sup>2</sup> appropriately, we observe that the
Euclidean distance in R<sup>2</sup> naturally appears in the asymptotics. We characterize this realization from a geometric view point of Kotani-Sunadafs
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 R<sup>2</sup>.
en-copyright=
kn-copyright=

en-aut-name=IshiwataSatoshi
en-aut-sei=Ishiwata
en-aut-mei=Satoshi
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

en-aut-name=KawabiHiroshi
en-aut-sei=Kawabi
en-aut-mei=Hiroshi
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=2
ORCID=

en-aut-name=TeruyaTsubasa
en-aut-sei=Teruya
en-aut-mei=Tsubasa
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=3
ORCID=

affil-num=1
en-affil=
kn-affil=Department of Mathematical Sciences, Faculty of Science Yamagata University

affil-num=2
en-affil=
kn-affil=Department of Mathematics, Faculty of Science Okayama University

affil-num=3
en-affil=
kn-affil=The Okinawa Kaiho Bank, Ltd.
en-keyword=Non-symmetric random walk
kn-keyword=Non-symmetric random walk
en-keyword=asymptotic expansion
kn-keyword=asymptotic expansion
en-keyword=triangular lattice
kn-keyword=triangular lattice
en-keyword=standard realization
kn-keyword=standard realization
END