The mixing time of a finite Markov chain counts the number of steps required for its distribution to approach its
stationary distribution from the worst
initial state. For a transition matrix 
and stationary
distribution 
,
the total variation convention is
 |
The frequently used threshold is 
. For an irreducible aperiodic finite
chain this time is finite. The choice of one step matters:
one coordinate sweep of the Thorp shuffle consists
of 
physical shuffles on 
cards.
Partial permutation information need not by itself determine the full law.
