LONG-TIME DERIVATION AT EQUILIBRIUM OF THE FLUCTUATING BOLTZMANN EQUATION

Thierry Bodineau; Isabelle Gallagher; Laure Saint-Raymon; Sergio Simonella

doi:10.1214/23-AOP1656

LONG-TIME DERIVATION AT EQUILIBRIUM OF THE FLUCTUATING BOLTZMANN EQUATION

Thierry Bodineau
, Isabelle Gallagher
, Laure Saint-Raymon
, Sergio Simonella

Université Paris-Saclay
Université PSL
Dipartimento di Matematica G. Castelnuovo
University of Rome

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study the deterministic evolution of a gas of hard spheres, initially distributed according to the equilibrium measure, and prove that, in the lowdensity limit, the fluctuation field converges to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times.

Original language	English
Pages (from-to)	217-295
Number of pages	79
Journal	Annals of Statistics
Volume	52
Issue number	1
DOIs	https://doi.org/10.1214/23-AOP1656
Publication status	Published - 1 Jan 2024
Externally published	Yes

Keywords

Fluctuating Boltzmann equation
low-density limit

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title = "LONG-TIME DERIVATION AT EQUILIBRIUM OF THE FLUCTUATING BOLTZMANN EQUATION",

abstract = "We study the deterministic evolution of a gas of hard spheres, initially distributed according to the equilibrium measure, and prove that, in the lowdensity limit, the fluctuation field converges to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times.",

keywords = "Fluctuating Boltzmann equation, low-density limit",

author = "Thierry Bodineau and Isabelle Gallagher and Laure Saint-Raymon and Sergio Simonella",

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AU - Bodineau, Thierry

AU - Gallagher, Isabelle

AU - Saint-Raymon, Laure

AU - Simonella, Sergio

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2024.

PY - 2024/1/1

Y1 - 2024/1/1

N2 - We study the deterministic evolution of a gas of hard spheres, initially distributed according to the equilibrium measure, and prove that, in the lowdensity limit, the fluctuation field converges to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times.

AB - We study the deterministic evolution of a gas of hard spheres, initially distributed according to the equilibrium measure, and prove that, in the lowdensity limit, the fluctuation field converges to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times.

KW - Fluctuating Boltzmann equation

KW - low-density limit

U2 - 10.1214/23-AOP1656

DO - 10.1214/23-AOP1656

M3 - Article

AN - SCOPUS:85186177328

SN - 0090-5364

VL - 52

SP - 217

EP - 295

JO - Annals of Statistics

JF - Annals of Statistics

IS - 1

ER -

LONG-TIME DERIVATION AT EQUILIBRIUM OF THE FLUCTUATING BOLTZMANN EQUATION

Abstract

Keywords

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