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Introduction to Renormalization

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2.2 Mathematics of coarse grained Markov chains » Quiz Solution

In the slippy counter, with probability ep (epsilon) for remaining in the same state, what's the probability that, if I begin in state A, I end up back in state A after three timesteps?

A. 

B.

C.

D.

 

Answer: (A). You can work this out in two ways. The quick way is to multiply the transition matrix against itself three times. The long way is to consider all the possible paths: A->A->A->A (probability ), A->B->A->A (probability ep(1-ep)^2) and so on.