Skip to Main content Skip to Navigation
Journal articles

Conditioned one-way simple random walk and representation theory

Abstract : 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].
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00670834
Contributor : Cédric Lecouvey <>
Submitted on : Thursday, February 16, 2012 - 11:13:55 AM
Last modification on : Wednesday, August 29, 2018 - 1:09:07 AM
Document(s) archivé(s) le : Thursday, May 17, 2012 - 2:26:55 AM

Files

SuperPathCrys150212.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00670834, version 1
  • ARXIV : 1202.3604

Collections

Citation

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

Share

Metrics

Record views

351

Files downloads

95