Large Deviation Principle for local empirical measure of Coulomb gases at intermediate temperature regime

Padilla‐Garza, David

doi:10.48550/arxiv.2011.00480

Cited by 2 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This raises the question of whether it would be possible to obtain results about the dynamical fluctuations of the empirical density without the hypothesis of a large plasma parameter limit. This is an interesting perspective that would extend our present work, and at the same time would extend the static picture discussed in [20,21,17].…”

Section: Discussionsupporting

confidence: 63%

“…In this paper, we obtained results quantifying the dynamical fluctuations of the empirical density of a Coulomb plasma in the large plasma parameter limit. A series of mathematical papers [20,21,17] focus on fluctuations of stationary observables for Coulomb gases without using the large plasma parameter limit. This raises the question of whether it would be possible to obtain results about the dynamical fluctuations of the empirical density without the hypothesis of a large plasma parameter limit.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical large deviations for plasmas below the Debye length and the Landau equation

Feliachi,

Bouchet

2021

Preprint

View full text Add to dashboard Cite

We consider a homogeneous plasma composed of N particles of the same electric charge which interact through a Coulomb potential. In the large plasma parameter limit, classical kinetic theories justify that the empirical density is the solution of the Balescu-Guernsey-Lenard equation, at leading order. This is a law of large numbers. The Balescu-Guernsey-Lenard equation is approximated by the Landau equation for scales much smaller than the Debye length. In order to describe typical and rare fluctuations, we compute for the first time a large deviation principle for dynamical paths of the empirical density, within the Landau approximation. We obtain a large deviation Hamiltonian that describes fluctuations and rare excursions of the empirical density, in the large plasma parameter limit. We obtain this large deviation Hamiltonian either from the Boltzmann large deviation Hamiltonian in the grazing collision limit, or directly from the dynamics, extending the classical kinetic theory for plasmas within the Landau approximation. We also derive the large deviation Hamiltonian for the empirical density of N particles, each of which is governed by a Markov process, and coupled in a mean field way. We explain that the plasma large deviation Hamiltonian is not the one of N particles coupled in a mean-field way.

show abstract

Section: Discussionsupporting

confidence: 63%

Section: Discussionmentioning

confidence: 99%

Dynamical large deviations for plasmas below the Debye length and the Landau equation

Feliachi,

Bouchet

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Apart from the microscopic and macroscopic scales, it is also possible to analyze rare events at a mesoscopic scale. In the Coulomb setting, this is the subject of [27]. In this case, the observable to analyze is the local empirical field, defined as…”

Section: For Any µmentioning

confidence: 99%

Large Deviations Principle for the tagged empirical field of a general interacting gas

Padilla‐Garza¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

This paper deals with rare events in a general interacting gas at high temperature. The main result is a Large Deviations Principle for the tagged empirical field, which features the competition of an energy term and an entropy term. The approach to proving this Large Deviations Principle is to first deduce one for the tagged empirical field of non-interacting particles at high temperature, and upgrade that result to interacting particle systems.

show abstract

Large Deviation Principle for local empirical measure of Coulomb gases at intermediate temperature regime

Cited by 2 publications

References 0 publications

Dynamical large deviations for plasmas below the Debye length and the Landau equation

Dynamical large deviations for plasmas below the Debye length and the Landau equation

Large Deviations Principle for the tagged empirical field of a general interacting gas

Contact Info

Product

Resources

About