Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations Article Swipe
Vivien Lecomte
,
Isabelle Gallagher
,
Laure Saint‐Raymond
,
Sergio Simonella
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.4007/annals.2023.198.3.3
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.4007/annals.2023.198.3.3
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square root of the average number of particles, converge to a Gaussian process driven by the fluctuating Boltzmann equation, as predicted in [67]; (2) large deviations are exponentially small in the average number of particles and are characterized, under regularity assumptions, by a large deviation functional as previously obtained in [61] for dynamics with stochastic collisions. The results are valid away from thermal equilibrium, but only for short times. Our strategy is based on uniform a priori bounds on the cumulant generating function, characterizing the fine structure of the small correlations.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.4007/annals.2023.198.3.3
- OA Status
- green
- Cited By
- 9
- References
- 43
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3081502418
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3081502418Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.4007/annals.2023.198.3.3Digital Object Identifier
- Title
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Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviationsWork title
- Type
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articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-10-26Full publication date if available
- Authors
-
Vivien Lecomte, Isabelle Gallagher, Laure Saint‐Raymond, Sergio SimonellaList of authors in order
- Landing page
-
https://doi.org/10.4007/annals.2023.198.3.3Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2008.10403Direct OA link when available
- Concepts
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Boltzmann equation, Dynamics (music), Statistical physics, Physics, Rare events, Hard spheres, Classical mechanics, Mathematics, Statistics, Thermodynamics, AcousticsTop concepts (fields/topics) attached by OpenAlex
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9Total citation count in OpenAlex
- Citations by year (recent)
-
2023: 1, 2022: 3, 2021: 2, 2020: 3Per-year citation counts (last 5 years)
- References (count)
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43Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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