A Glivenko-Cantelli Theorem for almost additive functions

Christoph Schumacher; Fabian Schwarzenberger; Ivan Veselic

doi:10.1016/j.spa.2016.06.005

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arXiv · 1606.07664

A Glivenko-Cantelli Theorem for almost additive functions

Christoph Schumacher·Fabian Schwarzenberger·Ivan Veselic

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Abstract

We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\,i.\,d.\ sequences of random variables indexed by~$\Z^d$. 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.

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BibTeX RIS

Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselic. 2016-06-24. A Glivenko-Cantelli Theorem for almost additive functions. https://doi.org/10.1016/j.spa.2016.06.005

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