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New steps in walks with small steps in the quarter plane

Irina Kourkova 1, * Kilian Raschel 2, *
* Corresponding author
1 Modélisation stochastique
LPMA - Laboratoire de Probabilités et Modèles Aléatoires
Abstract : In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite series, while in the literature, the standard expressions use solutions to boundary value problems. We illustrate our results with three examples (an algebraic case, a transcendental D-finite case, and an infinite group model).
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Submitted on : Saturday, September 20, 2014 - 8:29:03 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:08 PM
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Irina Kourkova, Kilian Raschel. New steps in walks with small steps in the quarter plane. Annals of Combinatorics, Springer Verlag, 2015, 19 (2015) (3), pp.461-511. ⟨10.1007/s00026-015-0279-4⟩. ⟨hal-00840239v2⟩



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