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.
