Probabilistic validation of homology computations for nodal domains

37. Konstantin Mischaikow, Thomas Wanner:
    Probabilistic validation of homology computations for nodal domains
    Annals of Applied Probability 17(3), pp. 980-1018, 2007.

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.

Links

The preprint version of the paper can be downloaded from https://arxiv.org/abs/0707.4588, while the published version of the paper can be found at https://doi.org/10.1214/105051607000000050.

Bibtex

@article{mischaikow:wanner:07a,
   author = {Konstantin Mischaikow and Thomas Wanner},
   title = {Probabilistic validation of homology computations for nodal domains},
   year = 2007,
   journal = {Annals of Applied Probability},
   volume = 17,
   number = 3,
   pages = {980--1018},
   doi = {10.1214/105051607000000050}
   }