Abstract
Ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a reversible random walk on an infinite graph satisfying a certain periodic condition. In the course of our argument, we employ perturbation theory for the maximal eigenvalues of twisted transition operator. As a result, an asymptotic of the probabilityp(n,x,y) that a particle starting atxreachesyat timenasngoes to infinity is established.
Original language | English |
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Pages (from-to) | 664-689 |
Number of pages | 26 |
Journal | Journal of Functional Analysis |
Volume | 159 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1998 Nov 10 |
Externally published | Yes |
Keywords
- Discrete Laplacian
- Discrete spectral geometry
- Random walk
- Transition probability
ASJC Scopus subject areas
- Analysis