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The compensation approach for walks with small steps in the quarter plane

Abstract : This paper is the first application of the compensation approach (a well-established theory in probability theory) to counting problems. We discuss how this method can be applied to a general class of walks in the quarter plane $Z_{+}^{2}$ with a step set that is a subset of $\{(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)\}$ in the interior of $Z_{+}^{2}$. We derive an explicit expression for the generating function which turns out to be nonholonomic, and which can be used to obtain exact and asymptotic expressions for the counting numbers.
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Submitted on : Thursday, July 4, 2013 - 1:50:18 PM
Last modification on : Thursday, March 5, 2020 - 5:33:44 PM
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Ivo Adan, Johan van Leeuwaarden, Kilian Raschel. The compensation approach for walks with small steps in the quarter plane. Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2013, 22 (2), pp.161-183. ⟨10.1017/S0963548312000594⟩. ⟨hal-00551472v3⟩

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