Computational Techniques in Theoretical Physics
Homework 9
 
  •  The transition probability W(i to j)  between 3 states is:
  •  
    W(1 to 1) = W(1 to 3) = 0, W(1 to 2) = 1

    W(2 to 1) = 1/6, W(2 to 2) = 1/2,
    W(2 to 3) = 1/3

    W(3 to 1)=0, W(3 to 2)=2/3, W(3 to 3) = 1/3

     
     
    (a)  Show that the solution for the probabilities is: (b)  Use P0=(1,0,0) as the initial distribution, how fast the system converges to the equilibrium probability distribution?
     
     
     
     
    (a) Is the Markov chain specified by the above transition probabilities ergodic?

    (b) Calculate the equilibrium probability distribution Pi, where i = 1,2,,3.

    (c) Does the equilibrium distribution satisfy detailed balance condition?