Fluctuations of lattice zonotopes and polygons
| Autor: | Buffière, Théophile, Marchal, Philippe |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. |
| Databáze: | arXiv |
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