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The threshold for integer homology in random d-complexes
Published 28 Aug 2013 in math.AT, math.CO, and math.PR | (1308.6232v2)
Abstract: Let Y ~ Y_d(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 H_{d-1}(Y; Z) is less than 80d log n / n. This bound is tight, up to a constant factor.
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