Work

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

Year: 2014

Type: article

Abstract: For a finite set of points P in R d , the function d P : R d → R + measures Euclidean distance to the set P. We study the number of critical points of d P when P is a Poisson process.In particular, we study the limit behavior of N k -the number of critical points of d P with Morse index k-as the density of points grows.We present explicit computations for the normalized limiting expectations and variances of the N k , as well as distributional limit theorems.We link these results to recent results in [16,17] in which the Betti numbers of the random Čech complex based on P were studied.

Source: Homology Homotopy and Applications

DOI: 10.4310/hha.2014.v16.n2.a18

Authors: Omer Bobrowski, Robert J. Adler

Institutions: Duke University, Technion – Israel Institute of Technology

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: Israel Academy of Sciences and Humanities, Air Force Office of Scientific Research, FP7 Information and Communication Technologies

Award: G503376696