Large fluctuations in the Hierarchical Coulomb gas

Seminar in Mathematics
The two-dimensional Coulomb gas model describes electrically charged particles embedded in a uniform background of the opposite charge, interacting through a logarithmic potential. A celebrated prediction from the physics literature, made by Jancovici, Lebowitz and Manificat in 1993, describes probabilities of observing large charge fluctuations in the system. From the mathematical standpoint, the JLM law is only proved in a very special 'solvable' case, with only partial results known in general.
A few years ago, Chatterjee introduced a hierarchical version of the Coulomb gas inspired by Dyson's hierarchical model for the Ising ferromagnet. In the talk, I will present an ongoing joint work with Alon Nishry, in which we prove that the JLM law holds for this Hierarchical Coulomb gas model.