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- W1520453355 abstract "In this paper we state the homological domination principle for random multi-parameter simplicial complexes, claiming that the Betti number in one specific dimension (which is explicitly determined by the probability multi-parameter) significantly dominates the Betti numbers in all other dimensions. We also state and discuss evidence for two interesting conjectures which would imply a stronger version of the homological domination principle, namely that generically homology of a random simplicial complex coincides with that of a wedges of k-dimensional spheres. These two conjectures imply that under an additional assumption (specified in the paper) a random simplicial complex collapses to a k-dimensional complex homotopy equivalent to a wedge of spheres of dimension k." @default.
- W1520453355 created "2016-06-24" @default.
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- W1520453355 date "2015-03-11" @default.
- W1520453355 modified "2023-10-16" @default.
- W1520453355 title "Homological Domination in Large Random Simplicial Complexes" @default.
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- W1520453355 doi "https://doi.org/10.48550/arxiv.1503.03253" @default.
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