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Journal Articles Journal of the European Mathematical Society Year : 2012

Counting walks in a quadrant: a unified approach via boundary value problems

Abstract

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations as well as on the sign of the covariance of the walk.
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Dates and versions

hal-00461853 , version 1 (06-03-2010)
hal-00461853 , version 2 (10-03-2010)
hal-00461853 , version 3 (17-02-2011)

Identifiers

  • HAL Id : hal-00461853 , version 3

Cite

Kilian Raschel. Counting walks in a quadrant: a unified approach via boundary value problems. Journal of the European Mathematical Society, 2012, 14, pp.749-777. ⟨hal-00461853v3⟩
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