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.

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)

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.

Source code for reproducing free random projection

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

Regression on LUE eigenvalues

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

Rocq proofs, checked by the kernel, of the sharp threshold for random ellipsoid fitting and of new results on optimal conditioning, mixtures, dependent laws and translated samples, with the reusable library GaussianAnalysis.

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.

Java project with a small matrix class hierarchy (general and tridiagonal) that studies how the variance of the determinant of a random matrix grows with size, using LU decomposition and a tridiagonal recurrence. Includes an interactive determinant calculator.

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).