Minimum Spanning Acycle and Lifetime of Persistent Homology in the Linial-Meshulam Process

摘要

This paper studies a higher dimensional generalization of Frieze's zeta(3)-limit theorem on the d-Linial-Meshulam process. First, we define spanning acycles as a higher dimensional analogue of spanning trees, and connect its minimum weight to persistent homology. Then, our main result shows that the expected weight of the minimum spanning acycle behaves in Theta(n(d-1)). (C) 2017 Wiley Periodicals, Inc.