Do there exist theorems for comparing frequencies in the stationary distribution of a (say) aperiodic, positive recurrent Markov chain? i.e. given the transition probability matrix $\mathbf{P}$ with stationary distribution $\boldsymbol{\pi}$, and given two states of interest, $i$ and $j$, are there properties of $\mathbf{P}$ that might imply that $\pi_i > \pi_j$? (Other than just $P_{ki} > P_{kj}$ for all $k$, of course!)
2026-03-26 03:00:41.1774494041
Comparing frequencies in stationary distribution
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