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Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths

Abstract : We introduce and characterize central probability distributions on Littelmann paths. Next we establish a law of large numbers and a central limit theorem for the generalized Pitmann transform. We then study harmonic functions on multiplicative graphs defined from the tensor powers of finite-dimensional Lie algebras representations. Finally, we show there exists an inverse of the generalized Pitman transform defined almost surely on the set of infinite paths remaining in the Weyl chamber and explain how it can be computed.
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https://hal.archives-ouvertes.fr/hal-01061664
Contributor : Cédric Lecouvey Connect in order to contact the contributor
Submitted on : Tuesday, February 24, 2015 - 11:10:54 AM
Last modification on : Friday, February 19, 2021 - 4:10:03 PM
Long-term archiving on: : Monday, May 25, 2015 - 10:31:10 AM

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  • HAL Id : hal-01061664, version 3
  • ARXIV : 1409.2334

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Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné. Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths. 2014. ⟨hal-01061664v3⟩

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