Counting walks in a quadrant: a unified approach via boundary value problems
By Kilian Raschel. 2010
70 citations recorded by the source corpus.
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
Subfields: Discrete Mathematics and Combinatorics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8f31c5866732ed65e1507baa37a590b8585b292a
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In Discrete Mathematics and Combinatorics
In Statistical and Nonlinear Physics
Citations in the corpus
- Random walks in cones (2011, result): “Raschel [40] and Kurkova and Raschel [34] also considered a two-dimensional random walk in the quarter plane, and proved some asymptotic results for the exit position.”
- On the functions counting walks with small steps in the quarter plane (2011, unknown): “For the 2 walks with infinite group on the left in Figure 2, they have been obtained in [20], by exploiting a particular property shared by the 5 models of Figure 2 commonly known as singular walks .”
- Random walks in the quarter plane, discrete harmonic functions and conformal mappings (2013, methodology): “This arises in probability theory [13, 14, 27], in queueing theory [7], in combinatorics [6, 26], etc.”