This material has been published in J. Physics Conf. Series 42 (2006), 179--212, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the Institute of Physics. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler

Watermelon configurations with wall interaction: exact and asymptotic results

(41 pages)

Abstract. We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start and end on the wall, and their mean number of contacts with the wall. We improve on the earlier (partially non-rigorous) results by Brak, Essam and Owczarek, providing new exact results, among which is a closed formula for the number of such watermelon configurations with a given number of contacts with the wall, and more precise asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.

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