Speaker: Nicolas Fraiman (University of North Carolina at Chapel Hill)
Title: Bulk and extremes of the weights of Minimal Spanning Acycles.
Speaker's URL: https://fraiman.web.unc.edu/
Abstract: A classic result by Frieze is that the total weight of the minimum spanning tree (MST) of the uniformly weighted graph converges to 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 analogue--the Minimum Spanning Acycle (MSA). In this talk, we look at the distribution of weights in this random MSA--both in the bulk and in the extremes. We show that the rescaled empirical distribution of weights in the MSA converges to a measure based on the density of the shadow – the object that generalizes the giant component in higher dimensions. We also show that the shifted extremal weights converge to an inhomogeneous Poisson point process. Our results also apply to the Linial-Meshulam model, where one has access only to a fraction of the potential face weights.
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