  We consider four examples of combinatorial triangles
$\left(T(n,k)\right)_{0\le k\le n}$ (Pascal, Stirling of both types, Euler) :
through saddle-point asymptotics, their \emph{Pascal's formulas} define four
vector fields, together with their field lines that turn out to be the
conjectured limit of sample paths of four well known Markov chains. We prove
this asymptotic behaviour in three of the four cases.
