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Random walks on periodic graphs
Author(s):
Takahiro
Kazami;
Kôhei
Uchiyama
Journal:
Trans. Amer. Math. Soc.
360
(2008),
6065-6087.
MSC (2000):
Primary 60G50;
Secondary 60J45
Posted:
June 16, 2008
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Abstract:
This paper concerns random walks on periodic graphs embedded in the  -dimensional Euclidian space  and obtains asymptotic expansions of the Green functions of them up to the second order term, which, expressed fairly explicitly, are easily computable for many examples. The result is used to derive an asymptotic form of the hitting distribution of a hyperplane of co-dimension one, which involves not only the first but also second order terms of the expansion of the Green function. We also give similar expansions of the transition probabilities of the walks.
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Additional Information:
Takahiro
Kazami
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro Tokyo, 152-8551 Japan
Email:
uchiyama@math.titech.ac.jp
Kôhei
Uchiyama
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro Tokyo, 152-8551 Japan
DOI:
10.1090/S0002-9947-08-04451-6
PII:
S 0002-9947(08)04451-6
Keywords:
Asymptotic expansion,
Markov additive process,
periodic graph,
Green function,
hitting distribution of a line
Received by editor(s):
July 26, 2006
Received by editor(s) in revised form:
November 21, 2006
Posted:
June 16, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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