Validity and and non-validity of propagation of chaos

K Matthies; F Theil

doi:10.1093/acprof:oso/9780199239252.003.0005

Validity and and non-validity of propagation of chaos

K Matthies, F Theil

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

3 Citations (SciVal)

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 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	https://doi.org/10.1093/acprof:oso/9780199239252.003.0005
Publication status	Published - Sept 2008

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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",

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AU - Theil, F

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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

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M3 - Chapter or section

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SP - 101

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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 -

Validity and and non-validity of propagation of chaos

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