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Journal Articles Combinatorics, Probability and Computing Year : 2013

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

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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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Dates and versions

hal-00551472 , version 1 (03-01-2011)
hal-00551472 , version 2 (07-10-2012)
hal-00551472 , version 3 (04-07-2013)

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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, 2013, 22 (2), pp.161-183. ⟨10.1017/S0963548312000594⟩. ⟨hal-00551472v3⟩
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