This paper studies a higher dimensional generalization of Frieze's$\zeta(3)$-limit theorem in the Erd\"os-R\'enyi graph process. Frieze's theoremstates that the expected weight of the minimum spanning tree converges to$\zeta(3)$ as the number of vertices goes to infinity. In this paper, we studythe $d$-Linial-Meshulam process as a model for random simplicial complexes,where $d=1$ corresponds to the Erd\"os-R\'enyi graph process. First, we definespanning acycles as a higher dimensional analogue of spanning trees, andconnect its minimum weight to persistent homology. Then, our main result showsthat the expected weight of the minimum spanning acycle behaves in$O(n^{d-1})$.
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