Decorrelation as an avatar of convexity

2015/07/02 by Mircea Petrache, Petrache, Mircea · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topology and Set Theory #Functional Equations Stability Results #Mathematical Dynamics and Fractals #math-ph #math.FA #math.MP #msc:26B25 #msc:42A82 #msc:46A55 #msc:49S99 #msc:81V55 #msc:82B05

paper · pdf · doi:10.48550/arxiv.1507.00782

8 pages. Comments are welcome!

arxiv created 2015/07/02 · arxiv updated 2015/07/06

Abstract

If X is a Polish space then we show that the product measure on X^∞ 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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