Conditioned one-way simple random walk and representation theory - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SLC Année : 2013

Conditioned one-way simple random walk and representation theory

Résumé

We call one-way simple random walk a random walk in the quadrant Z₊ⁿ whose increments belong to the canonical base. In relation with representation theory of Lie algebras and superalgebras, we describe the law of such a random walk conditioned to stay in a closed octant, a semi-open octant or other types of semi-groups. The combinatorial representation theory of these algebras allows us to describe a generalized Pitman transformation which realizes the conditioning on the set of paths of the walk. We pursue here in a direction initiated by O'Connell and his coauthors [13,14,2], and also developed in [12]. Our work relies on crystal bases theory and insertion schemes on tableaux described by Kashiwara and his coauthors in [1] and, very recently, in [5].
Fichier principal
Vignette du fichier
SuperPathCrys150212.pdf (310.23 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00670834 , version 1 (16-02-2012)

Identifiants

Citer

Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné. Conditioned one-way simple random walk and representation theory. SLC, 2013. ⟨hal-00670834⟩
209 Consultations
46 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More