4.1 Article

Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds

Related references

Note: Only part of the references are listed.
Article Statistics & Probability

FUNCTIONAL LIMIT THEOREMS FOR THE EULER CHARACTERISTIC PROCESS IN THE CRITICAL REGIME

Andrew M. Thomas et al.

Summary: This study presents functional limit theorems for the Euler characteristic of Vietoris-Rips complexes, focusing on points drawn from a nonhomogeneous Poisson process with highly connected and nontrivial topological characteristics. The study establishes two 'functional-level' limit theorems for the appropriately normalized Euler characteristic process, including a strong law of large numbers and a central limit theorem.

ADVANCES IN APPLIED PROBABILITY (2021)

Article Statistics & Probability

Convergence of persistence diagrams for topological crackle

Takashi Owada et al.

BERNOULLI (2020)

Article Physics, Mathematical

Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime

Akshay Goel et al.

JOURNAL OF STATISTICAL PHYSICS (2019)

Article Statistics & Probability

Topological crackle of heavy-tailed moving average processes

Takashi Owada

STOCHASTIC PROCESSES AND THEIR APPLICATIONS (2019)

Article Statistics & Probability

LIMIT THEOREMS FOR BETTI NUMBERS OF EXTREME SAMPLE CLOUDS WITH APPLICATION TO PERSISTENCE BARCODES

Takashi Owada

ANNALS OF APPLIED PROBABILITY (2018)

Article Statistics & Probability

LIMIT THEOREMS FOR POINT PROCESSES UNDER GEOMETRIC CONSTRAINTS (AND TOPOLOGICAL CRACKLE)

Takashi Owada et al.

ANNALS OF PROBABILITY (2017)

Article Statistics & Probability

Functional central limit theorem for subgraph counting processes

Takashi Owada

ELECTRONIC JOURNAL OF PROBABILITY (2017)

Article Statistics & Probability

The topology of probability distributions on manifolds

Omer Bobrowski et al.

PROBABILITY THEORY AND RELATED FIELDS (2015)

Article Computer Science, Theory & Methods

Crackle: The Homology of Noise

Robert J. Adler et al.

DISCRETE & COMPUTATIONAL GEOMETRY (2014)

Article Mathematics, Applied

DISTANCE FUNCTIONS, CRITICAL POINTS, AND THE TOPOLOGY OF RANDOM CECH COMPLEXES

Omer Bobrowski et al.

HOMOLOGY HOMOTOPY AND APPLICATIONS (2014)

Article Mathematics

EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY

Omer Bobrowski et al.

JOURNAL OF TOPOLOGY AND ANALYSIS (2012)

Article Computer Science, Theory & Methods

A TOPOLOGICAL VIEW OF UNSUPERVISED LEARNING FROM NOISY DATA

P. Niyogi et al.

SIAM JOURNAL ON COMPUTING (2011)

Editorial Material Mathematics

TOPOLOGY AND DATA

Gunnar Carlsson

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY (2009)

Article Computer Science, Theory & Methods

Finding the homology of submanifolds with high confidence from random samples

Partha Niyogi et al.

DISCRETE & COMPUTATIONAL GEOMETRY (2008)