HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Conditioned random walks from Kac-Moody root systems

Abstract : Random paths are time continuous interpolations of random walks. By using Littelmann path model, we associate to each irreducible highest weight module of a Kac Moody algebra g a random path W. Under suitable hypotheses, we make explicit the probability of the event E: W never exits the Weyl chamber of g. We then give the law of the random walk defined by W conditioned by the event E and proves this law can be recovered by applying to W the generalized Pitmann transform introduced by Biane, Bougerol and O'Connell. This generalizes the main results of [10] and [16] to Kac Moody root systems and arbitrary highest weight modules. Moreover, we use here a completely new approach by exploiting the symmetry of our construction under the action of the Weyl group of g rather than renewal theory and Doob's theorem on Martin kernels.
Complete list of metadata

Contributor : Cédric Lecouvey Connect in order to contact the contributor
Submitted on : Sunday, December 22, 2013 - 9:20:30 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:07 PM
Long-term archiving on: : Saturday, March 22, 2014 - 10:35:28 PM


Files produced by the author(s)


  • HAL Id : hal-00833657, version 3
  • ARXIV : 1306.3082



Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné. Conditioned random walks from Kac-Moody root systems. Transactions of the American Mathematical Society, American Mathematical Society, 2016. ⟨hal-00833657v3⟩



Record views


Files downloads