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The weakly dependent strong law of large numbers revisited
Abdelmalek Abdesselam · 2018-01-29 · via math.PR updates on arXiv.org

We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of convergence. Our proof does not use maximal inequalities and is instead inspired by the method of multiscale large versus small field decompositions in constructive quantum field theory.

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