Convex cones, integral zonotopes, limit shape

TL;DR

This paper proves that large integral zonotopes within convex cones tend to resemble a specific limit shape after scaling, and explores their combinatorial properties.

Contribution

It establishes the existence of a limit shape for large zonotopes in convex cones and analyzes their combinatorial characteristics.

Findings

Large zonotopes have a well-defined limit shape after scaling.

Most zonotopes are close to this limit shape.

Several combinatorial properties of large zonotopes are identified.

Abstract

This paper is about integral zonotopes. It is proven that large zonotopes in a convex cone have a limit shape, meaning that, after suitable scaling, the overwhelming majority of the zonotopes are very close to a fixed convex set. Several combinatorial properties of large zonotopes are established.