Large-N limit of the generalized 2D Yang-Mills theory on cylinder

Using the collective field theory approach of large-N generalized two-dimensional Yang-Mills theory on cylinder, it is shown that the classical equation of motion of collective field is a generalized Hopf equation. Then, using the Itzykson-Zuber integral at the large-N limit, it is found that the classical Young tableau density, which satisfies the saddle-point equation and determines the large-N limit of free energy, is the inverse of the solution of this generalized Hopf equation, at a certain point