Metric Markov cotype is a property of a metric space that controls the smoothing of functions on finite
reversible Markov chains. A metric
space 
has metric Markov cotype 
with constant 
if, for every positive integer 
and 
, every stochastic matrix 
with probability
vector 
satisfying 
,
and every 
,
..., 
,
there are 
,
..., 
such that
 |
The least possible 
is denoted 
(Mendel and Naor 2013). The points 
may leave the subset containing
the original 
,
which is why the property need not pass to subsets.
For 
,
this smoothing property supports Lipschitz
extension problem results with Hilbert space
sources.
