Validity and and non-validity of propagation of chaos

K Matthies, F Theil

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

In this chapter a novel, rigorous approach to analyse the validity of continuum approximations for deterministic interacting particle systems is discussed. The focus is on the Boltzmann–Grad limit of ballistic annihilation, a topic which has has received considerable attention in the physics literature. In this situation, due to the deterministic nature of the evolution, it is possible that correlations build up and the mean–field approximation by the Boltzmann equation breaks down. A sharp condition on the initial distribution, which ensures the validity of the Boltzmann equation is given, together with an example demonstrating the failure of the mean-field theory if the condition is viola
Original languageEnglish
Title of host publicationAnalysis and Stochastics of Growth Processes and Interface Models
EditorsP Mörter, R Moser, M Penrose, H Schwetlick, J Zimmer
PublisherOxford
Pages101-119
Number of pages19
ISBN (Print)978-0-19-923925-2
DOIs
Publication statusPublished - Sep 2008

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chaos
propagation
approximation
ballistics
breakdown
continuums
physics

Cite this

Matthies, K., & Theil, F. (2008). Validity and and non-validity of propagation of chaos. In P. Mörter, R. Moser, M. Penrose, H. Schwetlick, & J. Zimmer (Eds.), Analysis and Stochastics of Growth Processes and Interface Models (pp. 101-119). Oxford. https://doi.org/10.1093/acprof:oso/9780199239252.003.0005

Validity and and non-validity of propagation of chaos. / Matthies, K; Theil, F.

Analysis and Stochastics of Growth Processes and Interface Models. ed. / P Mörter; R Moser; M Penrose; H Schwetlick; J Zimmer. Oxford, 2008. p. 101-119.

Research output: Chapter in Book/Report/Conference proceedingChapter

Matthies, K & Theil, F 2008, Validity and and non-validity of propagation of chaos. in P Mörter, R Moser, M Penrose, H Schwetlick & J Zimmer (eds), Analysis and Stochastics of Growth Processes and Interface Models. Oxford, pp. 101-119. https://doi.org/10.1093/acprof:oso/9780199239252.003.0005
Matthies K, Theil F. Validity and and non-validity of propagation of chaos. In Mörter P, Moser R, Penrose M, Schwetlick H, Zimmer J, editors, Analysis and Stochastics of Growth Processes and Interface Models. Oxford. 2008. p. 101-119 https://doi.org/10.1093/acprof:oso/9780199239252.003.0005
Matthies, K ; Theil, F. / Validity and and non-validity of propagation of chaos. Analysis and Stochastics of Growth Processes and Interface Models. editor / P Mörter ; R Moser ; M Penrose ; H Schwetlick ; J Zimmer. Oxford, 2008. pp. 101-119
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