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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Minimal volume entropy for graphs


Author: Seonhee Lim
Journal: Trans. Amer. Math. Soc. 360 (2008), 5089-5100
MSC (2000): Primary 37A35, 20E08
Published electronically: May 14, 2008
MathSciNet review: 2415065
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Abstract: Among the normalized metrics on a graph, we show the existence and the uniqueness of an entropy-minimizing metric, and give explicit formulas for the minimal volume entropy and the metric realizing it.

Parmi les distances normalisées sur un graphe, nous montrons l'existence et l'unicité d'une distance qui minimise l'entropie, et nous donnons des formules explicites pour l'entropie volumique minimale et la distance qui la réalise.


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Additional Information

Seonhee Lim
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520-8283 – and – ENS-Paris, UMR 8553 CNRS, 45 rue d’Ulm, 75230 Paris Cedex 05, France
Address at time of publication: Department of Mathematics, Cornell University, 593 Malott Hall, Ithaca, New York 14853-4201
Email: seonhee.lim@yale.edu, Seonhee.Lim@ens.fr, slim@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04227-X
PII: S 0002-9947(08)04227-X
Received by editor(s): June 26, 2005
Received by editor(s) in revised form: December 3, 2005
Published electronically: May 14, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.