Given a transition matrix, is the biggest component of the stationary distribution the one that correspond to the column whose sum of entries is the biggest among all columns?
(By "correspond" I mean $ \text{The } i\text{th component of the vector} \leftrightarrow \text{the }i\text{th column of the matrix}$)
It seems plausible since in the transition matrix the column with the biggest sum of the entries is the most "absorbing" state. My probability teacher told me he often asks his colleagues about this fact, never hearing it is a known fact.