Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constant curvature metrics for Markov chains   We consider metrics which are preserved under a $p$-Wasserstein transport
map, up to a possible contraction. In the case $p=1$ this corresponds to a
metric which is uniformly curved in the sense of coarse Ricci curvature. We
investigate the existence of such metrics in the more general sense of
pseudo-metrics, where the distance between distinct points is allowed to be 0,
and show the existence for general Markov chains on compact Polish spaces.
Further we discuss a notion of algebraic reducibility and its relation to the
existence of multiple true pseudo-metrics with constant curvature. Conversely,
when the Markov chain is irreducible and the state space finite we obtain
effective uniqueness of a metric with uniform curvature up to scalar
multiplication and taking the $p$th root, making this a natural intrinsic
distance of the Markov chain. An application is given in the form of
concentration inequalities for the Markov chain.

5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn