Convex lattice polygonal lines with a constrained number of vertices

Julien Bureaux (1) , Nathanaël Enriquez (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

A detailed combinatorial analysis of planar convex lattice polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained.

Mots clés: convex polygons; grand canonical ensemble; zeta functions; local limit theorem; limit shape

Domaines: Probabilités [math.PR]

Julien Bureaux, Nathanaël Enriquez. Convex lattice polygonal lines with a constrained number of vertices. 2016. ⟨hal-01332360⟩