We study some examples of combinatorial triangles $(T(n,k))_{0\le k\le n}$ (e.g. Pascal's triangle, Stirling's triangles of both types, Euler's triangle) : each of their Pascal's formulas define a vector field, and its field lines, that turn out to be the limits of sample paths of well known Markov chains.

As an application to the asymptotic study of complete accessible automata, we provide a new derivation of a formula due to Korsunov. This is a joint work with Jules Flin and Alexis Zevio.