Minimum spanning acycle and lifetime of persistent homology in the Linial–Meshulam process1. Issue 2 (18th April 2017) - Hiraoka, Yasuaki; Shirai, Tomoyuki
Abstract: This paper studies a higher dimensional generalization of Frieze's ζ ( 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 Θ ( n d − 1 ) . © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 315–340, 2017