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Macroscopic and edge behavior of a planar jellium

Chafaï, Djalil; García-Zelada, David; Jung, Paul (2020), Macroscopic and edge behavior of a planar jellium, Journal of Mathematical Physics, 61, 3. 10.1063/1.5126724

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Journal of Mathematical Physics
Volume
61
Number
3
Publisher
American Institute of Physics
Published in
Paris
Publication identifier
10.1063/1.5126724
Metadata
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Author(s)
Chafaï, Djalil cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
García-Zelada, David
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Jung, Paul
Department of Mathematical Sciences, KAIST
Abstract (EN)
We consider a planar Coulomb gas in which the external potential is generated by a smeared uniform background of opposite-sign charge on a disc. This model can be seen as a two-dimensional Wigner jellium, not necessarily charge neutral, and with particles allowed to exist beyond the support of the smeared charge. The full space integrability condition requires low enough temperature or high enough total smeared charge. This condition does not allow at the same time, total charge neutrality and determinantal structure. The model shares similarities with both the complex Ginibre ensemble and the Forrester--Krishnapur spherical ensemble of random matrix theory. In particular, for a certain regime of temperature and total charge, the equilibrium measure is uniform on a disc as in the Ginibre ensemble, while the modulus of the farthest particle has heavy-tailed fluctuations as in the Forrester--Krishnapur spherical ensemble. We also touch on a higher temperature regime producing a crossover equilibrium measure, as well as a transition to Gumbel edge fluctuations. More results in the same spirit on edge fluctuations are explored by the second author together with Raphael Butez.
Subjects / Keywords
Coulomb gas; jellium; Ginibre ensemble; Forrester–Krishnapur spherical ensemble; large deviation principle; Gumbel law; heavy tail; determinantal point process

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