Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markov Type constants, flat tori and Wasserstein spaces   Let $M_p(X,T)$ denote the Markov type $p$ constant at time $T$ of a metric
space $X$, where $p \ge 1$. We show that $M_p(Y,T) \le M_p(X,T)$ in each of the
following cases: (a)$X$ and $Y$ are geodesic spaces and $Y$ is covered by $X$
via a finite-sheeted locally isometric covering, (b)$Y$ is the quotient of $X$
by a finite group of isometries, (c) $Y$ is the $L^p$-Wasserstein space over
$X$.
  As an application of (a) we show that all compact flat manifolds have Markov
type $2$ with constant $1$. In particular the circle with its intrinsic metric
has Markov type $2$ with constant $1$. This answers the question raised by
S.-I. Ohta and M. Pichot.
  Parts (b) and (c) imply new upper bounds for Markov type constants of the
$L^p$-Wasserstein space over $\mathbb R^d$. These bounds were conjectured by A.
Andoni, A. Naor and O. Neiman. They imply certain restrictions on bi-Lipschitz
embeddability of snowflakes into such Wasserstein spaces.

24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin