A probability vector is a vector 
of nonnegative real numbers whose coordinates
have sum 1, where 
is a positive integer.
It specifies a statistical distribution
on a finite set, with 
the probability of outcome
. The discrete
uniform distribution has 
.
For a Markov chain whose transition stochastic matrix 
has each row sum 1, a probability vector viewed as a row
vector is a stationary distribution
when 
. The detailed-balance
identities 
imply this stationarity and define reversibility
with respect to 
(Mendel and Naor 2013).
