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Creators/Authors contains: "Lancien, G."

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  1. ; ; ; (, Journal of the Institute of Mathematics of Jussieu)
    We prove that the class of reflexive asymptotic-$$c_{0}$$ Banach spaces is coarsely rigid, meaning that if a Banach space $$X$$ coarsely embeds into a reflexive asymptotic-$$c_{0}$$ space $$Y$$, then $$X$$ is also reflexive and asymptotic-$$c_{0}$$. In order to achieve this result, we provide a purely metric characterization of this class of Banach spaces. This metric characterization takes the form of a concentration inequality for Lipschitz maps on the Hamming graphs, which is rigid under coarse embeddings. Using an example of a quasi-reflexive asymptotic-$$c_{0}$$ space, we show that this concentration inequality is not equivalent to the non-equi-coarse embeddability of the Hamming graphs. 
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  2. ; ; (, Journal of the American Mathematical Society)
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