A Glivenko–Cantelli theorem for almost additive functions on lattices

Christoph Schumacher, Fabian Schwarzenberger and Ivan Veselić

Stochastic Processes and their Applications, 2017, vol. 127, issue 1, 179-208

Abstract: We develop a Glivenko–Cantelli theory for monotone, almost additive functions of i.i.d. sequences of random variables indexed by Zd. Under certain conditions on the random sequence, short range correlations are allowed as well. We have an explicit error estimate, consisting of a probabilistic and a geometric part. We apply the results to yield uniform convergence for several quantities arising naturally in statistical physics.

Keywords: Glivenko–Cantelli theory; Uniform convergence; Empirical measures; Large deviations; Statistical mechanics (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:1:p:179-208

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DOI: 10.1016/j.spa.2016.06.005

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