Work

On the vanishing of homology in random Čech complexes

Year: 2016

Type: article

Abstract: We compute the homology of random Čech complexes over a homogeneous Poisson process on the d-dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erdős -Rényi phase transition, where the Čech complex becomes connected. The second transition is where all the other homology groups are computed correctly (almost simultaneously). Our calculations also suggest a finer measurement of scales, where there is a further refinement to this picture and separation between different homology groups. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 14–51, 2017

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.20697

Authors: Omer Bobrowski, Shmuel Weinberger

Institutions: Technion – Israel Institute of Technology, University of Chicago

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Air Force Office of Scientific Research

Awards: Problems in Geometric, Algebraic and Quantitative Topology, Statistical and Applied Mathematical Sciences Institute, G5418073398