Random Matrix Eigenvalues (Multiple Distributions)     random-matrices

Leonid Petrov

This simulation uses WebAssembly and the Eigen library to compute eigenvalues of an N×N random matrix whose entries are drawn from one of the following distributions: uniform, exponential, Cauchy, Bernoulli, semicircle, each normalized to have mean 0 and variance (or nominal scale) 1/sqrt(N). Select the distribution below, choose a matrix size, and hit "Generate & Plot Eigenvalues" to see the resulting spectrum, top eigenvalues, a heatmap of the matrix, etc.

50  
Top 5 Eigenvalues:
5 Eigenvalues around zero:
Top 10 Eigenvalues (Point Process):
20 Eigenvalues Around Zero (Point Process):
Histogram of eigenvalues:
Heatmap of matrix elements:

code

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