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We consider dynamical transport metrics for probability measures on discretisations of a bounded convex domain in $\mathbb{R}^d$.
An optimal Poincaré inequality for convex domains
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Earlier work this paper cites.
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B. Grünbaum and G. C. Shephard · 1987
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E. B. Davies · 1989
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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