Year: 2023
Type: preprint
Abstract: We compute bounds in the expected Ollivier curvature for the Brownian continuum random tree $\mathcal{T}_{\mathbb{e}}$. The results indicate that when the scale dependence of the Ollivier curvature is properly taken into account, the Ollivier-Ricci curvature of $\mathcal{T}_{\mathbb{e}}$ is bounded above by every element of $\mathbb{R}$ for almost all points of $\mathcal{T}_{\mathbb{e}}$. This parallels the well-known result that every continuum tree is a $CAT(K)$ space for all $K\in\mathbb{R}$.
Source: arXiv (Cornell University)
Author: Kelly, Christy
Institution: RIKEN
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4389364258