Large deviation principle for geometric and topological functionals and associated point processes

Limit theory for U-statistics under geometric and topological constraints with rare events

(2022) Takashi Owada   JOURNAL OF APPLIED PROBABILITY

Convergence of persistence diagram in the sparse regime

(2022) Takashi Owada   ANNALS OF APPLIED PROBABILITY

Limit theorems for process-level Betti numbers for sparse and critical regimes

(2020) Takashi Owada et al.   ADVANCES IN APPLIED PROBABILITY

Localization in random geometric graphs with too many edges

(2020) Sourav Chatterjee et al.   ANNALS OF PROBABILITY

Limit theory for geometric statistics of point processes having fast decay of correlations

(2019) B. Błaszczyszyn et al.   ANNALS OF PROBABILITY

Concentration for Poisson U-statistics: Subgraph counts in random geometric graphs

(2017) Sascha Bachmann et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Functional Poisson approximation in Kantorovich–Rubinstein distance with applications to U-statistics and stochastic geometry

(2016) Laurent Decreusefond et al.   ANNALS OF PROBABILITY

On the topology of random complexes built over stationary point processes

(2015) D. Yogeshwaran et al.   ANNALS OF APPLIED PROBABILITY

Random geometric complexes in the thermodynamic regime

(2015) D. Yogeshwaran et al.   PROBABILITY THEORY AND RELATED FIELDS

Crackle: The Homology of Noise

(2014) Robert J. Adler et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Distance functions, critical points, and the topology of random Čech complexes

(2014) Omer Bobrowski et al.   Homology Homotopy and Applications

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

Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction

(2012) David Dereudre et al.   ELECTRONIC JOURNAL OF PROBABILITY

Topology and data

(2009) Gunnar Carlsson   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY