Semyon Klevtsov: Wiegmann–Zabrodin conjecture for \beta=1 in the hyperbolic case

Abstract: Wiegmann–Zabrodin conjecture concerns the \(O(1)\) terms in the large-N asymptotic expansion of the Coulomb gas partition function, or \(\beta\)-ensemble as it is also known for random matrices. The \(O(1)\) term is interesting because it reveals the gaussian free field, arising in the large N limit, and thus a correspondence with a 2d conformal field theory. In a particular case of \(\beta=1\) is determinantal. I will explain how to define the partition function in this case on Riemann surfaces, and how to obtain it’s asymptotics in the compact case. Then in the non-compact case I will compute the order \(O(1)\) term, which turns out to differ for compact case.

Work in common with P. Wiegmann.