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• W2963601914 abstract "We compute the homology of random Čech 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 -Rényi phase transition, where the Čech 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. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 14–51, 2017" @default.
• W2963601914 created "2019-07-30" @default.
• W2963601914 creator A5070671339 @default.
• W2963601914 creator A5073943501 @default.
• W2963601914 date "2016-11-07" @default.
• W2963601914 modified "2023-10-16" @default.
• W2963601914 title "On the vanishing of homology in random Čech complexes" @default.
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• W2963601914 doi "https://doi.org/10.1002/rsa.20697" @default.
• W2963601914 hasPublicationYear "2016" @default.
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