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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Transition Probabilities for Symmetric Jump Processes
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by Richard F. Bass and David A. Levin PDF
Trans. Amer. Math. Soc. 354 (2002), 2933-2953 Request permission

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.
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Additional 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