A Geometric study of Wasserstein spaces: Euclidean spaces

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A GEOMETRIC STUDY OF WASSERSTEIN SPACES: ULTRAMETRICS by Benôıt

— We study the geometry of the space of measures of a compact ultrametric space X , endowed with the L Wasserstein distance from optimal transportation. We show that the power p of this distance makes this Wasserstein space affinely isometric to a convex subset of l. As a consequence, it is connected by 1 p -Hölder arcs, but any α-Hölder arc with α > 1 p must be constant. This result is obtaine...

متن کامل

A Geometric Study of Wasserstein Spaces: An Addendum on the Boundary

We extend the geometric study of the Wasserstein space W2(X) of a simply connected, negatively curved metric space X by investigating which pairs of boundary points can be linked by a geodesic, when X is a tree. Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally compact metric space. Mainly, X is a space where triangles are “thin”: points on the opposite s...

متن کامل

Snowflake Universality of Wasserstein Spaces

For p ∈ (1,∞) let Pp(R) denote the metric space of all p-integrable Borel probability measures on R, equipped with the Wasserstein p metric Wp. We prove that for every ε > 0, every θ ∈ (0, 1/p] and every finite metric space (X, dX), the metric space (X, dX) embeds into Pp(R) with distortion at most 1 + ε. We show that this is sharp when p ∈ (1, 2] in the sense that the exponent 1/p cannot be re...

متن کامل

A Characterization of Euclidean Spaces

The purpose of this paper is to give an elementary proof of the fact that a Banach space in which there exist projection transformations of norm one on every two-dimensional linear subspace is a euclidean space. S. Kakutani [ l ] has pointed out that a modification of a proof due to Blaschke [2] will prove this theorem. F. Bohnenblust has been able to establish this theorem for the complex case...

متن کامل

Berkovich Spaces Embed in Euclidean Spaces

Let K be a eld that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analyti cation V an of any d-dimensional quasi-projective scheme V over K embeds in R. If, moreover, the value group of K is dense in R>0 and V is a curve, then we describe the homeomorphism type of V an by using the theory of local dendrites.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE

سال: 2010

ISSN: 2036-2145,0391-173X

DOI: 10.2422/2036-2145.2010.2.03