Séminaire du LPTMS: Bertrand Lacroix-à-chez-Toine *** séminaire exceptionnel ***


11:30 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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Extreme value statistics in a gas of 2D charged particles

Bertrand Lacroix-à-chez-Toine (LPTMS, Université Paris-Sud)


We study a system of N charged particles in two dimensions with Coulomb logarithmic repulsion and confined in an external symmetric potential. At the inverse temperature of interest β = 2, the positions of the charges form a 2D determinantal point process. In the case of a quadratic potential, there is a mapping between the positions of these charges and the eigenvalues of complex Ginibre matrices. We focus on the extremal statistics of the positions of the charges and in particular we highlight
a new universal regime (with respect to a large class of confining potentials) which had been overlooked before [1]. It allows to solve a puzzle of matching between the typical regime of fluctuations [2] and the large deviation regime [3]. Finally we also considered potentials that deviates from this universality class and computed the extremal statistics in these cases.

  • [1] B. Lacroix-A-Chez-Toine, A. Grabsch, S. N. Majumdar, G. Schehr, Extremes of 2d Coulomb gas: universal intermediate deviation regime, J. Stat. Mech. P013203, (2018).
  • [2] B. Rider, J. Phys. A 36(12), 3401 (2003).
  • [3] F. D. Cunden, F. Mezzadri, P. Vivo, J. Stat. Phys. 164(5), 1062-1081 (2016).
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