Proper gromov transforms of metrics are metrics
نویسندگان
چکیده
منابع مشابه
Proper gromov transforms of metrics are metrics
In phylogenetic analysis, a standard problem is to approximate a given metric by an additive metric. Here it is shown that, given a metric D defined on some finite set X and a non-expansive map f : X → R, the one-parameter family of the Gromov transforms D of D relative to f and ∆ that starts with D for large values of ∆ and ends with an additive metric for ∆ = 0 consists exclusively of metrics...
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This paper continues the investigation of ‘Wasserstein-like’ transportation distances for probability measures on discrete sets. We prove that the discrete transportation metrics on the d-dimensional discrete torus TN with mesh size 1 N converge, when N → ∞, to the standard 2-Wasserstein distance on the continuous torus in the sense of Gromov– Hausdorff. This is the first result of a passage to...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2002
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(02)00075-7