Talk:Markov chain mixing time

Where does the 1/4 come from? That seems arbitrary. Slaniel

It is arbitrary. Anything less than 1/2 will suffice. The point is to use submultiplicativity of total variation distance. Namely, if $$d(s)$$ denotes the variation distance after s steps, then $$d(s+t)\leq 2d(s)d(t)$$ (see Ch 2, Lemma 20 of Aldous & Fill's online text), and so if $$\tau$$ denotes the mixing time then $$d(k\tau)\leq 2^{k-1}d(\tau)^k \leq 1/2^{k+1}$$. kuroyama (talk) 14:13, 1 September 2008 (UTC)

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