Area limit laws for symmetry classes of staircase polygons

Abstract

We derive area limit laws for the various symmetry classes of staircase polygons on the square lattice, in a uniform ensemble where, for fixed perimeter, each polygon occurs with the same probability. This complements a previous study by Leroux and Rassart, where explicit expressions for the area and perimeter generating functions of these classes have been derived.

18 pages, 3 figures

References in corpus (6)

• Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas
• The first-passage area for drifted Brownian motion and the moments of the Airy distribution
• Scaling behaviour of two-dimensional polygon models
• Scaling function and universal amplitude combinations for self-avoiding polygons
• Singularity analysis, Hadamard products, and tree recurrences
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Cited by in corpus (1)

• On the joint distribution of the area and the number of peaks for Bernoulli excursions