  The two-dimensional one-component plasma (OCP) is a model of electrically
charged particles which are embedded in a uniform background of the opposite
charge, and interact through a logarithmic potential. More than 30 years ago,
Jancovici, Lebowitz and Manificat discovered an asymptotic law for
probabilities of large charge fluctuations in the OCP. We prove that this law
holds for the hierarchical counterpart of the OCP. The hierarchical model was
recently introduced by Chatterjee, and is inspired by Dyson's hierarchical
model of the Ising ferromagnet.
