Asymptotic expansion of the partition function for $\beta$-ensembles with complex potentials

Alice Guionnet, Karol Kozlowski, Alex Little

In this work we establish under certain hypotheses the $N\to +\infty$ asymptotic expansion of integrals of the form $$\mathcal{Z}_{N,Γ}[V] \, = \, \int_{Γ^N} \prod_{ a < b}^{N}(z_…