Eigenvalue histogram for Wigner random matrices with selectable entry distributions (uniform, exponential, Cauchy, Bernoulli, semicircle), overlaid with the semicircle law curve. Point process scatter plots show top 10 and 20 near-zero eigenvalues. A color heatmap displays matrix entries. Adjust matrix size N and distribution type.
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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.
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)-
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)