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Drilling holes in the Brownian disk: The Brownian annulus

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arxiv 2407.13544 v1 pith:SJZSQGNJ submitted 2024-07-18 math.PR

Jean-François Le Gall , Alexis Metz-Donnadieu This is my paper · ORCID
classification math.PR
keywords brownianannulusboltzmanncenteredconstructiondiskdistinguishedprove
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We give a new construction of the Brownian annulus based on removing a hull centered at the distinguished point in the free Brownian disk. We use this construction to prove that the Brownian annulus is the scaling limit of Boltzmann triangulations with two boundaries. We also prove that the space obtained by removing hulls centered at the two distinguished points of the Brownian sphere is a Brownian annulus. Our proofs rely on a detailed analysis of the peeling by layers algorithm for Boltzmann triangulations with a boundary.

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  1. The scaling limit of planar maps with large faces

    math.PR 2025-01 accept novelty 8.0 of 10

    Large Boltzmann planar maps with a stable exponent alpha converge in the Gromov-Hausdorff-Prokhorov sense to an explicit random compact metric space S_alpha of Hausdorff dimension 2 alpha.

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