Scatter plot of corner eigenvalues for complex Hermitian ensembles with outlier perturbations. Choose 10-point atomic, GUE, or rotated GUE regimes, each with up to 5 outlier eigenvalue inputs. In atomic mode, drag red points or edit fields to set the spectrum. Adjust matrix size N up to 500 and click Resample.
Skip to simulation visualization
This page computes eigenvalues of successive top-left corners of three different complex Hermitian random-matrix ensembles (each with an option to add up to five outliers).
- 10-Point Atomic: a diagonal matrix with 10 distinct eigenvalues (each repeated proportionally in size \(N\)), plus 5 outliers in the last 5 diagonal entries, all conjugated by a random complex unitary.
- GUE: a complex Hermitian GUE matrix + a rank $\le 5$ perturbation in the first 5 diagonal entries.
- Rotated GUE: a random complex Hermitian GUE matrix + a rank-5 diagonal perturbation \(U D U^\dagger\), where \(D\) has up to 5 outliers. The difference with the previous ensemble is that the perturbation is free with respect to the original GUE matrix.
Adjust \(N\) (up to 500) and outlier values, then click “Resample” to see the corner eigenvalue scatter plot.
Simulation Regime:
Outlier Values (up to 5)
50
Corner Eigenvalue Plot
code
(note: parameters in the code might differ from the ones in simulation results below)-
Link to code(Interactive simulation (JavaScript & Emscripten)) -
Link to code(C++ source code compiled to WebAssembly)