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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2016

Conditioned random walks from Kac-Moody root systems

Résumé

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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Dates et versions

hal-00833657 , version 1 (13-06-2013)
hal-00833657 , version 2 (18-10-2013)
hal-00833657 , version 3 (22-12-2013)

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