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arXiv · 2508.21416

Dynamics from iterated averaging

Tobias Fritz·Nicolás Rivera
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Abstract

We prove that for a standard Lebesgue space $X$, the strong operator closure of the semigroup generated by conditional expectations on $L^\infty(X)$ contains the group of measure-preserving automorphisms. This is based on a solution to the following puzzle: given $n$ full water tanks, each containing one unit of water, and $n$ empty ones, how much water can be transferred from the full tanks to the empty ones by repeatedly equilibrating the water levels between pairs of tanks?

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Tobias Fritz, Nicolás Rivera. 2025-08-29. Dynamics from iterated averaging. https://arxiv.org/abs/2508.21416

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