Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process
Yasuaki Hiraoka, Tomoyuki Shirai · Random Structures and Algorithms · 2017
This paper studies a higher dimensional generalization of Frieze's -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 . © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 315–340, 2017