Christian Krattenthaler: Asymptotic Analysis of Stars and Watermelons

This is a joint work with Tony Guttmann and Xavier Viennot.

"Stars" and "watermelons" are objects which are frequently studied in statistical mechanics. They are special instances of Michael Fisher's "vicious walkers" model, which is a model of walkers on a lattice which never occupy the same point at a given time. I shall present results on the asymptotic behaviour of stars and watermelons. In the derivations we shall meet some (of my) friends which are usually not so often seen in asymptotic analysis, such as Schur functions, symplectic characters, Macdonald-Mehta integrals, and basic hypergeometric series.

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