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• W1914945357 abstract "We compute the homology of random Cech complexes over a homogeneous Poisson process on the d-dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erdős-Renyi phase transition, where the Cech complex becomes connected. The second transition is where all the other homology groups are computed correctly (almost simultaneously). Our calculations also suggest a finer measurement of scales, where there is a further refinement to this picture and separation between different homology groups." @default.
• W1914945357 created "2016-06-24" @default.
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• W1914945357 date "2015-07-24" @default.
• W1914945357 modified "2023-09-27" @default.
• W1914945357 title "On the Vanishing of Homology in Random v{C}ech Complexes" @default.
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