Corner eigenvalues of orthogonally invariant random matrices with fixed spectrum     random-matrices

Connor MacMahon, Leonid Petrov

This simulation computes the eigenvalues of successive corners of a random matrix. You can choose between two regimes:

  • GOE: The matrix is generated as a random Gaussian Orthogonal Ensemble (GOE) matrix.
  • Discrete Top Eigenvalue Profile: A diagonal matrix with 10 distinct eigenvalues (each with high multiplicity) is conjugated by a random Haar matrix. You can adjust the 10 discrete eigenvalues by dragging the red points or by using the numeric fields below.

Use the slider to set the matrix size \(N\) (maximum 300), then click “Resample” to generate a new simulation.

Simulation Regime:
  
Discrete Top Eigenvalue Profile (Drag the red points):

Drag the 10 red points horizontally to set the 10 distinct eigenvalues.

Discrete Profile Values
50  
Corner Eigenvalue Dot Plot:

code

(note: parameters in the code might differ from the ones in simulation results below)