In this talk, we consider a model of 2d one component plasma, i.e. a gas of identical negatively charged particles. These charges are at equilibrium at inverse temperature B in an external containing potential created by a positive charge smeared over the two dimensional plane. For specific potentials and temperatures, this problem is connected to the study of eigenvalues of non-Hermitian random matrices, to the quantum fluctuations of fermions in a rotating harmonic trap or in a Laughlin state. We study the extreme value statistics for this system as well as the full counting statistics, i.e. the number of charges in a given domain of space. For both these observables, the regime of typical fluctuations [1] and the large deviation regime [2, 3] have been characterized.
While one would naively expect a smooth matching between these regimes, as it is the case for example for observables of Hermitian random matrices, it is not the case here. We solve this puzzle by showing that for both cases, an intermediate regime" of fluctuations emerges and characterize it in detail [4, 5]. This regime is universal with respect to a large class of confining potential. We have also considered potentials that do not enter this class and shown that there are cases where an intermediate regime of fluctuation does not appear.
References
[1] T. Shirai, J. Stat. Phys. 123, 615 (2006).
[2] R. Allez, J. Touboul, G. Wainrib, J. Phys. A: Math. Theor. 47, 042001
(2014).
[3] F. D. Cunden, F. Mezzadri, P. Vivo, J. Stat. Phys. 164, 1062 (2016).
[4] B. Lacroix-A-Chez-Toine, A. Grabsch, S. N. Majumdar, G. Schehr, J. Stat.
Mech.: Theory Exp. 013203 (2018).
