2022
DOI: 10.48550/arxiv.2203.10806
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Elongated Poisson-Voronoi cells in an empty half-plane

Abstract: The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane of R 2 gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges of these cells is ruled by a Markovian branching mechanism which is asymptotically described by two sequences of iid variables which are respectively Beta and exponentially distributed. This leads to a precise description of the scaling limit of a so-called typical cell. The limit object is a random apeirogon that we name men… Show more

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