Topological Expansion in the Complex Cubic Log-Gas Model. One-Cut Case

Pavel M. Bleher, Alfredo Deaño, Maxim Yattselev

We prove the topological expansion for the cubic log-gas partition function \[ Z_N(t)= \int_Γ\cdots\int_Γ\prod_{1\leq j<k\leq N}(z_j-z_k)^2 \prod_{k=1}^Ne^{-N\left(-\frac{z^3}{3}+t…