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Brownian geometry

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Japanese Journal of Mathematics Aims and scope

Abstract

We present different continuous models of random geometry that have been introduced and studied in recent years. In particular, we consider the Brownian sphere (also called the Brownian map), which is the universal scaling limit of large planar maps in the Gromov-Hausdorff sense, and the Brownian disk, which appears as the scaling limit of planar maps with a boundary. We discuss the construction of these models, and we emphasize the role played by Brownian motion indexed by the Brownian tree.

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Acknowledgements

It is a pleasure to thank the organizers of the Takagi Lectures for giving me the opportunity to discuss the present work at this prestigious meeting.

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Authors and Affiliations

  1. Institut de Mathématique d’Orsay-Bâtiment 307, Université Paris-Sud, 91405, Orsay Cedex, France

    Jean-François Le Gall

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  1. Jean-François Le Gall
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Correspondence to Jean-François Le Gall.

Additional information

Communicated by: Takashi Kumagai

This article is based on the 21st Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on June 23, 2018.

Supported by the ERC Advanced Grant 740943 GeoBrown

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Le Gall, JF. Brownian geometry. Jpn. J. Math. 14, 135–174 (2019). https://doi.org/10.1007/s11537-019-1821-7

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  • DOI: https://doi.org/10.1007/s11537-019-1821-7

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