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We present some results connecting Littelmann paths and Brownian paths in the framework of affine Kac–Moody algebras. We prove in particular that the string coordinates associated to a sequence of random Littelmann paths previously introduced by Cédric Lecouvey, Emmanuel Lesigne and Marc Peigné, converge towards their analogs for Brownian paths. At the end, we conjecture a Pitman-type theorem for a Brownian motion in an affine Weyl chamber that would generalize a previous one obtained for \(A_1^1\) .

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Brownian Paths in an Affine Weyl Chamber and Littelmann Paths

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  • 发表日期：

    2025年

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  • Manon Defosseux

摘要

We present some results connecting Littelmann paths and Brownian paths in the framework of affine Kac–Moody algebras. We prove in particular that the string coordinates associated to a sequence of random Littelmann paths previously introduced by Cédric Lecouvey, Emmanuel Lesigne and Marc Peigné, converge towards their analogs for Brownian paths. At the end, we conjecture a Pitman-type theorem for a Brownian motion in an affine Weyl chamber that would generalize a previous one obtained for \(A_1^1\) .