Random walks in Weyl chambers and crystals

DOI10.1112/plms/pdr033zbMath1242.17011arXiv1010.2341OpenAlexW2027180732MaRDI QIDQ3116525

Marc Peigné, Cédric Lecouvey, Emmanuel Lesigne

Publication date: 24 February 2012

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2341

zbMATH Keywords

generalized Pitman transformKashiwara crystal basesrandom walks on Euclidean latticesrandom walks on Weyl chambers

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Renewal theory (60K05)

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Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths ⋮ Quantum \(SL_2\), infinite curvature and Pitman's $2M-X$ theorem ⋮ Duality and bicrystals on infinite binary matrices ⋮ Geometric RSK and the Toda lattice ⋮ Large tensor products and Littlewood-Richardson coefficients ⋮ Conditioned random walks from Kac-Moody root systems ⋮ Central measures on multiplicative graphs, representations of Lie algebras and weight polytopes ⋮ The invariant measure of PushASEP with a wall and point-to-line last passage percolation ⋮ Stochastic differential equations for Lie group valued moment maps ⋮ t-Martin Boundary of Killed Random Walks in the Quadrant

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