This material has been published in
J. Physics Conf. Series 42 (2006), 179--212,
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Watermelon configurations with wall interaction:
exact and asymptotic results
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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