Probabilistic validation of homology computations for nodal domains
Abstract
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study based on suitable discretizations. Such an approach immediately raises the question of how accurate the resulting homology computations are. In this paper, we present a probabilistic approach to quantifying the validity of homology computations for nodal domains of random fields in one and two space dimensions, which furnishes explicit probabilistic a priori bounds for the suitability of certain discretization sizes. We illustrate our results for the special cases of random periodic fields and random trigonometric polynomials.
Keywords
Cite
@article{arxiv.0707.4588,
title = {Probabilistic validation of homology computations for nodal domains},
author = {Konstantin Mischaikow and Thomas Wanner},
journal= {arXiv preprint arXiv:0707.4588},
year = {2020}
}
Comments
Published at http://dx.doi.org/10.1214/105051607000000050 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)