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Preprint Number 2286

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2286. Amador Martin-Pizarro, Daniel Palacin and Julia Wolf
Stability, corners, and other 2-dimensional shapes

Submission date: 25 October 2022


We introduce a relaxation of stability, called robust stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a pseudofinite group. We show that robust stability satisfies a stationarity principle for measure independent elements. We apply this principle to deduce the existence of squares and $L$-shapes in dense subsets of Cartesian squares of pseudofinite groups, possibly non-abelian. Our results imply qualitative asymptotic versions for Cartesian squares of finite groups.

Mathematics Subject Classification: 03C13, 03C45, 11B30

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Full text arXiv 2210.14039: pdf, ps.

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