Large deviations for subcomplex counts and Betti numbers in multiparameter simplicial complexes
Abstract
We consider the multiparameter random simplicial complex as a higher dimensional extension of the classical Erdős–Rényi graph. We investigate appearance of “unusual” topological structures in the complex from the point of view of large deviations. We first study upper tail large deviation probabilities for subcomplex counts, deriving the order of magnitude of such probabilities at the logarithmic scale precision. The obtained results are then applied to analyze large deviations for the number of simplices of the multiparameter simplicial complexes. Finally, these results are also used to deduce large deviation estimates for Betti numbers of the complex in the critical dimension.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 16, 2023
- Source ID
- 10.1002/rsa.21146
Entities
People
- Gennady Samorodnitsky
- Takashi Owada
Organizations
- Air Force Office of Scientific Research
- Cornell University
- National Science Foundation
- Purdue University