Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal transport between random measures   We study couplings $q^\bullet$ of two equivariant random measures
$\lambda^\bullet$ and $\mu^\bullet$ on a Riemannian manifold $(M,d,m)$. Given a
cost function we ask for minimizers of the mean transportation cost per volume.
In case the minimal/optimal cost is finite and $\lambda^\omega\ll m$ we prove
that there is a unique equivariant coupling minimizing the mean transportation
cost per volume. Moreover, the optimal coupling is induced by a transportation
map, $q^\bullet=(id,T)_*\lambda^\bullet.$ We show that the optimal
transportation map can be approximated by solutions to classical optimal
transportation problems on bounded regions. In case of $L^p-$cost the optimal
transportation cost per volume defines a metric on the space of equivariant
random measure with unit intensity.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg