{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:O257SOOK4MQTPDICBABYJGOKAR","short_pith_number":"pith:O257SOOK","schema_version":"1.0","canonical_sha256":"76bbf939cae321378d0208038499ca046f60dd142aeb3669942aae5817f6a562","source":{"kind":"arxiv","id":"1610.04886","version":4},"attestation_state":"computed","paper":{"title":"Markov Type constants, flat tori and Wasserstein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Vladimir Zolotov","submitted_at":"2016-10-16T16:46:38Z","abstract_excerpt":"Let $M_p(X,T)$ denote the Markov type $p$ constant at time $T$ of a metric space $X$, where $p \\ge 1$. We show that $M_p(Y,T) \\le M_p(X,T)$ in each of the following cases: (a)$X$ and $Y$ are geodesic spaces and $Y$ is covered by $X$ via a finite-sheeted locally isometric covering, (b)$Y$ is the quotient of $X$ by a finite group of isometries, (c) $Y$ is the $L^p$-Wasserstein space over $X$.\n  As an application of (a) we show that all compact flat manifolds have Markov type $2$ with constant $1$. In particular the circle with its intrinsic metric has Markov type $2$ with constant $1$. 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We show that $M_p(Y,T) \\le M_p(X,T)$ in each of the following cases: (a)$X$ and $Y$ are geodesic spaces and $Y$ is covered by $X$ via a finite-sheeted locally isometric covering, (b)$Y$ is the quotient of $X$ by a finite group of isometries, (c) $Y$ is the $L^p$-Wasserstein space over $X$.\n  As an application of (a) we show that all compact flat manifolds have Markov type $2$ with constant $1$. In particular the circle with its intrinsic metric has Markov type $2$ with constant $1$. 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