Crackle: The Homology of Noise

The topology of probability distributions on manifolds

(2014) Omer Bobrowski et al.   PROBABILITY THEORY AND RELATED FIELDS

Limit theorems for Betti numbers of random simplicial complexes

(2013) Matthew Kahle et al.   Homology Homotopy and Applications

Collapsibility and Vanishing of Top Homology in Random Simplicial Complexes

(2012) Lior Aronshtam et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Random Geometric Complexes

(2011) Matthew Kahle   DISCRETE & COMPUTATIONAL GEOMETRY

A Topological View of Unsupervised Learning from Noisy Data

(2011) P. Niyogi et al.   SIAM JOURNAL ON COMPUTING

The fundamental group of random $2$-complexes

(2010) Eric Babson et al.   JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

Topology and data

(2009) Gunnar Carlsson   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

Finding the Homology of Submanifolds with High Confidence from Random Samples

(2008) Partha Niyogi et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Homological connectivity of randomk-dimensional complexes

(2008) R. Meshulam et al.   RANDOM STRUCTURES & ALGORITHMS