Article Dans Une Revue Journal of the European Mathematical Society Année : 2012

Counting walks in a quadrant: a unified approach via boundary value problems

Résumé

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations as well as on the sign of the covariance of the walk.

Fichier principal
Vignette du fichier
CountingWalksRaschel.pdf (387.66 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-00461853 , version 1 (06-03-2010)
hal-00461853 , version 2 (10-03-2010)
hal-00461853 , version 3 (17-02-2011)

Licence

Identifiants

  • HAL Id : hal-00461853 , version 3

Citer

Kilian Raschel. Counting walks in a quadrant: a unified approach via boundary value problems. Journal of the European Mathematical Society, 2012, 14, pp.749-777. ⟨hal-00461853v3⟩
455 Consultations
483 Téléchargements

Partager

  • More