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- Title
On the vanishing of homology in random Čech complexes.
- Authors
Bobrowski, Omer; Weinberger, Shmuel
- Abstract
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
- Subjects
HOMOLOGY theory; RANDOM data (Statistics); POISSON processes; PHASE transitions; TOPOLOGY
- Publication
Random Structures & Algorithms, 2017, Vol 51, Issue 1, p14
- ISSN
1042-9832
- Publication type
Article
- DOI
10.1002/rsa.20697