The expected total curvature of random polygons

Curvature of random walks and random polygons in confinement

The purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere. Curvature is one of several basic geometric properties that can be used to describe random walks and polygons. We show that confinement affects curvature quite strongly, and in the limit case where the confinement diameter equals the edge length the unconfined expected cur...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Generating Random Orthogonal Polygons

We propose two different methods for generating random orthogonal polygons with a given number of vertices. One is a polynomial time algorithm and it is supported by a technique we developed to obtain polygons with an increasing number of vertices starting from a unit square. The other follows a constraint programming approach and gives great control on the generated polygons. In particular, it...

Knotted polygons with curvature in Z 3

The knot probability of semiflexible polygons on the cubic lattice is investigated. The degree of stiffness of the polygon is mimicked by introducing a bending fugacity conjugate to the curvature of the polygon. By generalizing Kesten’s pattern theorem to semiflexible walks, we show that for any finite value of the bending fugacity all except exponentially few sufficiently long polygons are kno...

Heuristics for the Generation of Random Polygons

We consider the problem of randomly generating simple polygons on a given set of points. This problem is of considerable importance in the practical evaluation of algorithms that operate on polygons, where it is necessary to check the correctness and to determine the actual CPU-consumption of an algorithm experimentally. We rst present an approach by O'Rourke and Virmani (1991). Next, we discus...