The Harer–Zagier recursion for 1-point correlation functions

The Harer–Zagier recursion relations are famous linear recursion relations enabling constructing genus expansion of 1-point correlation functions to extremely high genera for a regular spectral curve (the Gaussian model). I describe the Brezin–Hikami replica method for deriving these relations and its generalizations to irregular spectral curves (Laguerre and generalized Laguerre ensembles) and how it is related to colorings of Riemann surfaces