The snake in the Brownian sphere

Omer Angel, Emmanuel Jacob, Brett Kolesnik, Grégory Miermont

The snake in the Brownian sphere: 2 upvotes on Hugging Face Daily Papers, #30 of 33 papers on 2025-02-25. Day-by-day upvote history.

The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere.

Paper page on Hugging Face · arXiv

Data: hysts-bot-data/daily-papers-stats and the Daily Papers API. Open data: tardellirs/paper-pulse-data. Sister project: Model Pulse, the download history of every model on the Hub.