A probability vector is a vector 
of nonnegative real
numbers whose coordinates sum to one. It specifies a statistical
distribution on a finite set, with 
the probability of outcome
.
The uniform distribution has 
.
For a Markov chain with transition stochastic matrix 
,
a row probability vector is stationary when 
. The detailed-balance identities 
imply this stationarity and define reversibility
with respect to 
(Mendel and Naor 2013).
