C Krattenthaler 2006 J. Phys.: Conf. Ser. 42 179 doi:10.1088/1742-6596/42/1/017
Watermelon configurations with wall interaction: exact and asymptotic results
C Krattenthaler
Show affiliationsWe 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 on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general 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.
- PACS
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05.40.Fb Random walks and Levy flights
02.10.Ox Combinatorics; graph theory
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Issue 1 (2006)
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Watermelon configurations with wall interaction: exact and asymptotic results
C Krattenthaler 2006 J. Phys.: Conf. Ser. 42 179
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