Résumé : In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths or random walks, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not have the same intuitive probabilistic behaviour as classical Dyck paths (the typical properties of which are strongly related to Brownian motion theory). In this talk we will quantify some relations between these two types of paths. Starting from an a priori not expected continued fraction (for which we give a bijective proof, and an analytic proof), we prove several formulae for related combinatorial structures conjectured in the On-line Encyclopedia of Integer Sequences. We also derive limit laws for parameters like the number of returns to zero or the size of an average catastrophe. We end with some considerations on uniform random generation. [Joint work with Cyril Banderier]
Dernière modification : Wednesday 23 August 2017 | Contact : Cyril.Banderier at lipn.univ-paris13.fr |