Algebraic generating functions for two-dimensional random walks

Abstract : In this paper, we caracterize the solutions of specific bi-variate functional equations. The unknown functions represent the steady state distribution of specific two-dimensional random walks on Z2+. Inside the quarter plane, the jump have amplitude one, but are arbitrary on the axes. The main result is a necessary and sufficient condition for the solutions to be algebraic, when the "group" of the random walk (associated to an algebraic curve Q(x,y) = 0 having genus one) is finite. The method is based on Hilbert's factorization theorems, together with a uniformisation by means of elliptic functions.
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Rapport
RR-1184, INRIA. 1990
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https://hal.inria.fr/inria-00075374
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Dernière modification le : vendredi 16 septembre 2016 - 15:11:36
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Guy Fayolle, Roudolph Iasnogorodski, Vadim A. Malyshev. Algebraic generating functions for two-dimensional random walks. RR-1184, INRIA. 1990. 〈inria-00075374〉

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