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- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
- Subject
- Mathematics; Mathematics, general
- ISSN
- 2199-6792
- eISSN
- 2199-6806
- DOI
- 10.1007/s40598-016-0062-6
- Publisher site
- See Article on Publisher Site
Abstract
We study random, finite-dimensional, ungraded chain complexes over a finite field and show that for a uniformly distributed differential a complex has the smallest possible homology with the highest probability: either zero or one-dimensional homology depending on the parity of the dimension of the complex. We prove that as the order of the field goes to infinity the probability distribution concentrates in the smallest possible dimension of the homology. On the other hand, the limit probability distribution, as the dimension of the complex goes to infinity, is a super-exponentially decreasing, but strictly positive, function of the dimension of the homology.
Journal
Arnold Mathematical Journal – Springer Journals
Published: Jan 25, 2017