A random hermitian matrix representation for two-dimensional percolation model‎

In this letter, the random matrix theory representation of a bond-percolation model on square lattice is presented. The behavior can be determined only by its two largest eigenvalues. second eigenvalue sits exactly edge semicircle part eigenvalue’s distribution and position function p, other hand first disjointed from eigenvalues Gaussian. Also responsible for scaling properties near criticality. Numerical simulations show power-law divergences emerged coalescence critical point at thermodynamic limit. letter formalism presented which describes complete fluctuations with set exponents in finite-size systems.