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By Lecturer Prof, Alistair Sinclair, Scribes Alistair Sinclair and F F (x

Abstract

Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. They may be distributed outside this class only with the permission of the Instructor. 9.1 Random function representation Let P be an ergodic Markov chain on state space Ω. Recall the “random function ” representation of P, namely as a probability distribution over functions f: Ω → Ω such that where the probability is over the random choice of f. Pr[f(x) = y] = P (x, y) ∀x, y, (9.1

Year: 2011
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