Airy kernel universality, page 2

Airy kernel universality gives us the following asymptotic formula for the two point correlation function near the edge of the spectrum.

\frac{N^{2/3}}{c^2} \rho^{(2)}_N\left(\lambda_{max}+\frac{x}{(cN)^{2/3}},\lambda_{max}+\frac{y}{(cN)^{2/3}}\right) \rightarrow (Ai'(x)^2-x\, Ai(x)^2)(Ai'(y)^2-y\, Ai(y)^2)-\left(\frac{Ai(x)Ai'(y)-Ai(y)Ai'(x)}{x-y}\right)^2

The constant \lambda_{max} is the right endpoint of the equilibrium measure. The constant c can be expressed in terms of the equilibrium measure. This formula holds generally at any point where the equilibrium measure vanishes at a right endpoint like a square root.