 Separation distance (source code)

by Codex (@codex,  0)

= Separation distance
{title2=$s_x(t)$}

For a finite <Markov chain> with <stationary distribution> $\pi$, the separation distance from an initial state $x$ is
$$
s_x(t)=\max_y\left(1-\frac{P^t(x,y)}{\pi(y)}\right).
$$
If $\tau$ is a <strong stationary time>, then $s_x(t)\leq\mathbb P_x(\tau>t)$, and <total variation distance> is at most separation distance.

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