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### Modulus of of continuity of a convolution operator with respect to Wasserstein metric

For a (discrete) measure $G$ on some reasonable metric space $\Theta$, consider the map $G \mapsto f_G$ defined as
$$
f_G := f*G(dx) := \int f(dx|\theta) G(d\theta)
$$
for some nice kernel function ...

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### Constructing a family of domains for application of method of continuity in optimal transportation

Anyway can help me about this paper?
http://arxiv.org/pdf/math/0601086v4.pdf
I want to ask page 20, The author want to construct a family of subdomain for using method of continuity. But I can't ...

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204 views

### 1-Wasserstein distance between two multivariate normal

The $p$-Wasserstein between two measures $\nu_1$ and $\nu_2$ on $X$ is given by
...

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**1**answer

155 views

### $X$ Polish geodesic implies $(P_2(X), W_2)$ geodesic

If $X,d$ is a complete and separable space then the space of Borel probability measures with finite second moment on $X$ endowed with the Wasserstein distance $W_2$ is geodesic.
I am looking for ...

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75 views

### a generalization of Monge-Kantorovich Problem

I am thinking about the martingale version of Monge-Kantorovich Problem.
Let $\mu(x)$ and $\nu(y)$ denote two density laws on $\mathbb{R}$, and define $M(\mu,\nu)$ the set of densities $f(x,y)$ on ...

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138 views

### Tangential boundary regularity for optimal transport maps

I'm interested in (and a bit confused by) the following theorem of Caffarelli, proven in section $4$ of his paper Boundary regularity of maps with convex potentials II:
Assume $u$ is a convex ...

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158 views

### Where to use differential calculus on space of measures?

One great inside of Felix Otto is that the Wasserstein metric from optimal transportation gives the space of (finite second moment, probability) measures on $\mathbb{R}^n$ (or a manifold) a kind of ...