### Abstract

Original language | English |
---|---|

Title of host publication | Analysis and Stochastics of Growth Processes and Interface Models |

Editors | P Mörter, R Moser, M Penrose, H Schwetlick, J Zimmer |

Publisher | Oxford |

Pages | 101-119 |

Number of pages | 19 |

ISBN (Print) | 978-0-19-923925-2 |

DOIs | |

Publication status | Published - Sep 2008 |

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### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Analysis and Stochastics of Growth Processes and Interface Models.*Oxford, pp. 101-119. https://doi.org/10.1093/acprof:oso/9780199239252.003.0005

}

TY - CHAP

T1 - Validity and and non-validity of propagation of chaos

AU - Matthies, K

AU - Theil, F

PY - 2008/9

Y1 - 2008/9

N2 - 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

AB - 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

U2 - 10.1093/acprof:oso/9780199239252.003.0005

DO - 10.1093/acprof:oso/9780199239252.003.0005

M3 - Chapter

SN - 978-0-19-923925-2

SP - 101

EP - 119

BT - Analysis and Stochastics of Growth Processes and Interface Models

A2 - Mörter, P

A2 - Moser, R

A2 - Penrose, M

A2 - Schwetlick, H

A2 - Zimmer, J

PB - Oxford

ER -