Limit distributions and scaling functions

Details Limit distributions and scaling functions Limit distributions and scaling functions

2007-04-05

arxiv.org/abs/0704.0716v4

Physics

Mathematical Physics

54 pages, 2 figures; v2 updated and slightly expanded; v3 changes in some proofs; v4 slightly expanded

Scientific paper

We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs with the same probability. We relate limit distributions to the scaling behaviour of the associated perimeter and area generating functions, thereby providing a geometric interpretation of scaling functions. To a major extent, this article is a pedagogic review of known results.

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