Calculus of Variations and Geometric Measure Theory
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M. Petrache

Decorrelation as an avatar of convexity

created by petrache on 10 Jul 2015

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Submitted Paper

Inserted: 10 jul 2015
Last Updated: 10 jul 2015

Pages: 8
Year: 2015

Abstract:

If $X$ is a Polish space then we show that the product measure on $X^\infty$ is guaranteed to minimize $c$-energy amongst exchangeable measures with fixed marginals if and only if the interaction kernel $c$ defines a convex energy functional on probability measures. A reformulation of this condition close to the theory of positive definite functions is highlighted.


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