Random walks on periodic graphs
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- by Takahiro Kazami and Kôhei Uchiyama PDF
- Trans. Amer. Math. Soc. 360 (2008), 6065-6087 Request permission
Abstract:
This paper concerns random walks on periodic graphs embedded in the $d$-dimensional Euclidian space $\mathbf {R}^d$ 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.References
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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
- Received by editor(s): July 26, 2006
- Received by editor(s) in revised form: November 21, 2006
- Published electronically: June 16, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 6065-6087
- MSC (2000): Primary 60G50; Secondary 60J45
- DOI: https://doi.org/10.1090/S0002-9947-08-04451-6
- MathSciNet review: 2425703