增强的Forman曲率及其与Ollivier曲率的关系
Enhanced Forman curvature and its relation to Ollivier curvature
摘要：
涌现几何和量子引力离散化方法的最新进展依赖于图曲率的离散度量的概念。我们专注于两个主要的措施，已被研究，所谓的奥利维尔-里奇和福曼-里奇曲率。这两种方法有着非常不同的起源，并且都有优点和缺点。在这项工作中，我们研究了这两个措施之间的关系，一类图是重要的量子引力的应用。我们发现，在一组特定的情况下，它们是等价的，潜在地打开了利用这两种方法在涌现时空和量子引力模型中的相对优势的可能性。
英文摘要：
Recent advances in emergent geometry and discretized approaches to quantum gravity have relied upon the notion of a discrete measure of graph curvature. We focus on the two main measures that have been studied, the so-called Ollivier-Ricci and Forman-Ricci curvatures. These two approaches have a very different origin, and both have advantages and disadvantages. In this work we study the relationship between the two measures for a class of graphs that are important in quantum gravity applications. We discover that under a specific set of circumstances they are equivalent, potentially opening up the possibility of exploiting the relative strengths of both approaches in models of emergent spacetime and quantum gravity.
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