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arXiv · 2404.18489

Peeling the Brownian half-plane

Jean-François Le Gall·Armand Riera
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Abstract

We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped with an intrinsic metric is still a Brownian half-plane, which is independent of the part that has been removed. This is an analog of the well-known peeling procedure for random planar maps. We also investigate several distributional properties of hulls centered at a boundary point, and we provide a new construction of the Brownian half-plane giving information about distances from a half-boundary.

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Jean-François Le Gall, Armand Riera. 2024-04-29. Peeling the Brownian half-plane. https://arxiv.org/abs/2404.18489

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