Transition Probabilities for Symmetric Jump Processes
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- by Richard F. Bass and David A. Levin
- Trans. Amer. Math. Soc. 354 (2002), 2933-2953
- DOI: https://doi.org/10.1090/S0002-9947-02-02998-7
- Published electronically: March 11, 2002
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Abstract:
We consider symmetric Markov chains on the integer lattice in $d$ dimensions, where $\alpha \in (0,2)$ and the conductance between $x$ and $y$ is comparable to $|x-y|^{-(d+\alpha )}$. We establish upper and lower bounds for the transition probabilities that are sharp up to constants.References
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Bibliographic Information
- Richard F. Bass
- Affiliation: Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269
- Email: bass@math.uconn.edu
- David A. Levin
- Affiliation: Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269
- Address at time of publication: P.O. Box 368, Annapolis Junction, Maryland 20701-0368
- Email: levin@member.ams.org
- Received by editor(s): June 18, 2001
- Received by editor(s) in revised form: December 27, 2001
- Published electronically: March 11, 2002
- Additional Notes: Research of the first author was partially supported by NSF grant DMS-9988496
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 2933-2953
- MSC (2000): Primary 60J05; Secondary 60J35
- DOI: https://doi.org/10.1090/S0002-9947-02-02998-7
- MathSciNet review: 1895210