Pascal's formulas and vector fields
Combinatorics
2023-09-18 v2
Abstract
We consider four examples of combinatorial triangles (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.
Keywords
Cite
@article{arxiv.2210.11814,
title = {Pascal's formulas and vector fields},
author = {Philippe Chassaing and Jules Flin and Alexis Zevio},
journal= {arXiv preprint arXiv:2210.11814},
year = {2023}
}