Suppose we have a stochastic matrix, $M$, representing the flow across some network. The upper-right element $M|_{1,n}$ is the probability to move from event $1$ to event $n$ in a given time-step. I want to put an upper bound on the probability to move from event $1$ to event $n$ in $k$ time-steps. i.e. find some $b$ such that
$$M^k|_{1,n} \leq b$$
for all $k$. Is it possible to do this in terms of the elements of $M$?