random-matrices

Parallel random matrix tools and complexity for deep learning

Leymosun Science: Quantum Research Toolkit

Random matrix theory of polarized light scattering in disordered media

simply create random matrices.

The random matrix gallery is a curated display of classes of random matrices where the eigenvalue spectrum is known. Each image in the gallery below links to a dedicated python notebook where you can vary the parameters and explore the effect on the resulting spectrum.

Python scripts from paper Optimal cleaning for singular values of cross-covariance matrices, by Florent Benaych-Georges, Jean-Philippe Bouchaud, Marc Potters (see https://arxiv.org/abs/1901.05543)

Source code for reproducing free random projection

Regression on LUE eigenvalues

Python tools for finite free probability, random matrix sampling and spectral computation.

Circular law for sparse random matrices with independent row slices at sufficiently large logarithmic degree, with Lean 4/mathlib proofs, manuscript, and reproducible verification.

25 mathematical candidate conjectures, six priority research leads, illustrated explanations, and reproducible evidence. Proofs, counterexamples, and literature welcome.

A Python package for numerical work with random matrix ensembles, with a particular focus on the Gaussian, Laguerre, Jacobi, and Circular beta ensembles. The package implements spectrum generation for general Dyson index beta.

Code, data, figures and manuscript for "Multifractal Large Deviations in Quantum Entanglement: Ideal Fermi-Gas Mapping, Markov Tensor Cascades, and Quartic Casimir Symmetry" (R. Chen, 2026).