Corner eigenvalues of GOEs and orthogonally invariant random matrices with fixed spectrum random-matrices
Connor MacMahon, Leonid Petrov
Scatter plot of eigenvalues from successive top-left corners of an orthogonally invariant random matrix, showing interlacing patterns. Choose GOE or discrete top eigenvalue profile regime. In discrete mode, drag 10 red control points or edit numeric fields to set the spectrum. Adjust matrix size N up to 300 and click Resample.
Skip to simulation visualization
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)-
Link to code(This simulation is interactive, written in JavaScript – see the source code of this page at the link) -
Link to code(C++ code for the simulation)