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            <funder>The research leading to this work was supported by a Subagreement from the Johns Hopkins University with funds provided by Grant No. 663054 from Simons Foundation</funder>
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            <idno type="halRefHtml">&lt;i&gt;Journal of Statistical Physics&lt;/i&gt;, 2021, 183, pp.article number 42. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s10955-021-02771-9"&gt;&amp;#x27E8;10.1007/s10955-021-02771-9&amp;#x27E9;&lt;/a&gt;</idno>
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            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-ORLEANS">Université d'Orléans</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
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            <idno type="stamp" n="IDP">Institut Denis Poisson</idno>
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            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
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                <term xml:lang="en">Balescu-Guernsey-Lenard equation</term>
                <term xml:lang="en">Large deviation theory</term>
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              <p>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.</p>
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