Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Martingale Wasserstein inequality for probability measures in the convex
  order   It was shown by the authors that two one-dimensional probability measures in
the convex order admit a martingale coupling with respect to which the integral
of $\vert x-y\vert$ is smaller than twice their $\mathcal W_1$-distance
(Wasserstein distance with index $1$). We showed that replacing $\vert
x-y\vert$ and $\mathcal W_1$ respectively with $\vert x-y\vert^\rho$ and
$\mathcal W_\rho^\rho$ does not lead to a finite multiplicative constant. We
show here that a finite constant is recovered when replacing $\mathcal
W_\rho^\rho$ with the product of $\mathcal W_\rho$ times the centred $\rho$-th
moment of the second marginal to the power $\rho-1$. Then we study the
generalisation of this new stability inequality to higher dimension.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess