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Cyclical monotonicity and the ergodic theorem

Published online by Cambridge University Press:  09 January 2014

MATHIAS BEIGLBÖCK
MATHIAS BEIGLBÖCK*
Affiliation:
Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria email mathias.beiglboeck@univie.ac.at
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Abstract

It is well known that optimal transport plans are cyclically monotone. The reverse implication that cyclically monotone transport plans are optimal needs some assumptions and the proof is non-trivial even if the costs are given by the squared euclidean distance on ${ \mathbb{R} }^{n} $. We establish this result as a corollary to the ergodic theorem.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 3 , May 2015 , pp. 710 - 713
Copyright
© Cambridge University Press, 2014 

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