We construct a Markov chain with three states a 0 = 0, a 1 = c 0 • √ d and a 2 = c 1 • √ d governed by the following transition distribution: Let X t be the state at time t. The principal eigenvector of the transition matrix ( 1 3 , 1 3 , 1 3 ) gives the stationary probability distribution of X t .
x t ∈ {a 1 , a 2 } with probability 2 3 .