Asymptotics of convex lattice polygonal lines with a constrained number of vertices

Julien Bureaux (1) , Nathanaël Enriquez (1)

1 MODAL'X - Modélisation aléatoire de Paris X

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.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; local limit theorem

Domaines: Probabilités [math.PR]

Julien Bureaux, Nathanaël Enriquez. Asymptotics of convex lattice polygonal lines with a constrained number of vertices. Israel Journal of Mathematics, 2017, 222 (2), pp.515-549. ⟨10.1007/s11856-017-1599-3⟩. ⟨hal-01705821⟩