Fluctuations of lattice zonotopes and polygons
Probability
2023-04-03 v1
Abstract
Following Barany et al., who proved that large random lattice zonotopes converge to a deterministic shape in any dimension after rescaling, we establish a central limit theorem for finite-dimensional marginals of the boundary of the zonotope. In dimension 2, for large random convex lattice polygons contained in a square, we prove a Donsker-type theorem for the boundary fluctuations, which involves a two-dimensional Brownian bridge and a drift term that we identify as a random cubic curve.
Keywords
Cite
@article{arxiv.2303.18045,
title = {Fluctuations of lattice zonotopes and polygons},
author = {Théophile Buffière and Philippe Marchal},
journal= {arXiv preprint arXiv:2303.18045},
year = {2023}
}