The threshold for integer homology in random d-complexes
Abstract
Let Y ~ Yd(n,p) denote the Bernoulli random d-dimensional simplicial complex. We answer a question of Linial and Meshulam from 2003, showing that the threshold for vanishing of homology Hd-1(Y; Z) is less than 80d log n / n. This bound is tight, up to a constant factor.
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