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 (4)

• 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
• Singularity analysis, Hadamard products, and tree recurrences
• On q-functional equations and excursion moments

Cited by in corpus (1)

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