Dynamics from iterated averaging
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912841421815808 |
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| author | Fritz, Tobias Rivera, Nicolás |
| author_facet | Fritz, Tobias Rivera, Nicolás |
| contents | 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? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21416 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics from iterated averaging Fritz, Tobias Rivera, Nicolás Dynamical Systems Probability Primary: 37A05. Secondary: 60A10, 80M50 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? |
| title | Dynamics from iterated averaging |
| topic | Dynamical Systems Probability Primary: 37A05. Secondary: 60A10, 80M50 |
| url | https://arxiv.org/abs/2508.21416 |