Brownian geometry
Probability
2018-10-08 v1
Abstract
We present different continuous models of random geometry that have been introduced and studied in the recent years. In particular, we consider 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.
Keywords
Cite
@article{arxiv.1810.02664,
title = {Brownian geometry},
author = {Jean-François Le Gall},
journal= {arXiv preprint arXiv:1810.02664},
year = {2018}
}
Comments
Survey paper written for the 21st Takagi lectures