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.
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Transactions of the American Mathematical Society, American Mathematical Society, 2016
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Contributeur : Cédric Lecouvey <>
Soumis le : dimanche 22 décembre 2013 - 09:20:30
Dernière modification le : mercredi 29 août 2018 - 01:09:08
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  • HAL Id : hal-00833657, version 3
  • ARXIV : 1306.3082

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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〉

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