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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Scaling coupling of reflecting Brownian motions and the hot spots problem
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by Mihai N. Pascu PDF
Trans. Amer. Math. Soc. 354 (2002), 4681-4702 Request permission

Abstract:

We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetric second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.
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Additional Information
  • Mihai N. Pascu
  • Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
  • Address at time of publication: Department of Mathematics, Purdue Uniwersity, West Lafayette, Indiana 47907-1395
  • Email: pascu@math.purdue.edu
  • Received by editor(s): September 9, 2001
  • Received by editor(s) in revised form: January 12, 2002
  • Published electronically: May 7, 2002
  • Additional Notes: I would like to thank Richard Bass, Krzysztof Burdzy, Nicolae N. Pascu and Nicolae R. Pascu for several helpful discussions
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 4681-4702
  • MSC (2000): Primary 60J65; Secondary 60J45, 35B05, 35K05
  • DOI: https://doi.org/10.1090/S0002-9947-02-03020-9
  • MathSciNet review: 1926894