Staircase polygons: moments of diagonal lengths and column heights

Details Staircase polygons: moments of diagonal lengths and column heights Staircase polygons: moments of diagonal lengths and column heights

2006-05-30

arxiv.org/abs/math-ph/0605076v1

J. Phys.: Conf. Ser. 42 (2006), 239-257

Physics

Mathematical Physics

24 pages, 7 figures; to appear in proceedings of Counting Complexity: An International Workshop On Statistical Mechanics And C

Scientific paper

10.1088/1742-6596/42/1/022

We consider staircase polygons, counted by perimeter and sums of k-th powers of their diagonal lengths, k being a positive integer. We derive limit distributions for these parameters in the limit of large perimeter and compare the results to Monte-Carlo simulations of self-avoiding polygons. We also analyse staircase polygons, counted by width and sums of powers of their column heights, and we apply our methods to related models of directed walks.

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