Probabilistic validation of homology computations for nodal domains

Konstantin Mischaikow, Thomas Wanner

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)980-1018
Number of pages39
JournalAnnals of Applied Probability
Issue number3
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Fields
  • Homology
  • Nodal domains
  • Random


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