Asymptotics for Beta-Ensembles at High Temperature
A talk in the Seminar Zufallsmatrizen series by
Charlie Dworaczek Guera
| Abstract: | In the high-temperature regime for β-ensembles, the inverse temperature is set as β=O(1/N). In this setting, the entropic effects due to the integration Lebesgue measure play on the same scale as the energy. Due to a simultaneous energy minimization-entropy maximization, it results in the non-compactness of the support of the equilibrium measure. In previous research, in collaboration with Ronan Memin (IMT), we proved a CLT for linear statistics in this regime by inverting the master operator, which is a central object in the study of the fluctuations. In this presentation, I will demonstrate how to employ the loop equations analysis method to establish the existence of an asymptotic expansion for the log partition function. We will see how certain aspects of the proof are significantly more complex compared to the classical regime. Within the CRC this talk is associated to the project(s): C6 |