Non-asymptotic equivalence between $W_2$ distance and $\dot{H}^{-1}$ norm

Details Non-asymptotic equivalence between $W_2$ distance and $\dot{H}^{-1}$ norm Non-asymptotic equivalence between $W_2$ distance and $\dot{H}^{-1}$ norm

2011-04-24

arxiv.org/abs/1104.4631v1

Mathematics

Functional Analysis

5 pages

Scientific paper

It is well known that the quadratic Wasserstein distance $W_2(\cdot,\cdot)$
is formally equivalent to the $\dot{H}^{-1}$ homogeneous Sobolev norm for
infinitesmially small perturbations. In this article I show that this
equivalence can be integrated to get non-asymptotic comparison results between
these distances.

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