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arXiv · 2303.18045

Fluctuations of lattice zonotopes and polygons

Théophile Buffière·Philippe Marchal
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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.

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Théophile Buffière, Philippe Marchal. 2023-03-31. Fluctuations of lattice zonotopes and polygons. https://arxiv.org/abs/2303.18045

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