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- W4307680652 abstract "The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space $E$, one can associate an $R$-tree called the continuous cactus of $E$. We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov-Hausdorff sense. Moreover, the Brownian cactus can be interpreted as the continuous cactus of the so-called Brownian map." @default.
- W4307680652 created "2022-11-04" @default.
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- W4307680652 date "2011-02-21" @default.
- W4307680652 modified "2023-09-27" @default.
- W4307680652 title "The Brownian Cactus I. Scaling limits of discrete cactuses" @default.
- W4307680652 doi "https://doi.org/10.48550/arxiv.1102.4177" @default.
- W4307680652 hasPublicationYear "2011" @default.
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