تقرير
Oliver Curvature Bounds for the Brownian Continuum Random Tree
العنوان: | Oliver Curvature Bounds for the Brownian Continuum Random Tree |
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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 |
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