تقرير
Oliver Curvature Bounds for the Brownian Continuum Random Tree
| العنوان: | Oliver Curvature Bounds for the Brownian Continuum Random Tree |
|---|---|
| المؤلفون: | Kelly, Christy |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Metric Geometry, 49Q22 (Primary), 51F99 (Secondary) |
| الوصف: | 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 $K\in\mathbb{R}$. Comment: 20 pages, 1 appendix |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.01894 |
| رقم الأكسشن: | edsarx.2312.01894 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |