The Bulk and the Extremes of Minimal Spanning Acycles and Persistence Diagrams of Random Complexes
The expected weight of the Minimum Spanning Tree (MST) in a uniformly weighted graph on $n$ vertices converges to the constant $\zeta(3).$ Recently, this result was extended to a uniformly weighted simplicial complex, where the role of the MST is played by its higher-dimensional analog: the Minimum Spanning Acycle (MSA). Our work goes beyond and provides a complete description of the histogram of weights in this random MSA as also the death times in the associated persistence diagram.
References:
Skraba P, Thoppe G, Yogeshwaran D. Randomly weighted d-complexes: Minimal spanning acycles and Persistence diagrams. Electronic Journal of Combinatorics. 2020 Apr 17;27(2).
Fraiman N, Mukherjee S, Thoppe G. The Bulk and the Extremes of Minimal Spanning Acycles and Persistence Diagrams of Random Complexes. arXiv preprint arXiv:2012.14122. 2020 Dec 28.
