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Area-perimeter generating functions of lattice walks: q-series and their asymptotics

Prellberg, T (QMUL)
Wednesday 01 July 2009, 11:30-12:00

Seminar Room 1, Newton Institute


We present results on the generating function of a lattice model of an adsorbing polymer, realised as partially directed walks above a skewed line, weighted with respect to the number of contacts and the enclosed area. The solution is in form of a quotient of two q-Bessel functions, and the singular limit as q approaches 1 is of fundamental importance in the phase diagram of the model.


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