EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY

DOI10.1142/S1793525312500057zbMath1260.60070arXiv1003.5175WikidataQ125824150 ScholiaQ125824150MaRDI QIDQ2885380

Matthew Strom Borman, Omer Bobrowski

Publication date: 23 May 2012

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.5175

zbMATH Keywords

Euler characteristicrandom fieldsBetti numberspersistent homologybarcodesGaussian kinematic formula

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Sample path properties (60G17) Other homology theories in algebraic topology (55N35)

Related Items (8)

A central limit theorem for the Euler integral of a Gaussian random field ⋮ Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds ⋮ Mean geometry for 2D random fields: level perimeter and level total curvature integrals ⋮ Persistent magnitude ⋮ A Fractal Dimension for Measures via Persistent Homology ⋮ Topological data analysis of noise: uniform unimodal distributions ⋮ Hadwiger's theorem for definable functions ⋮ The topology of probability distributions on manifolds

Cites Work

• A statistical approach to persistent homology
• A Gaussian kinematic formula
• Validity of the expected Euler characteristic heuristic
• Euler integration over definable functions
• Target Enumeration via Euler Characteristic Integrals
• Topology and data
• Barcodes: The persistent topology of data

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