Random Matrix Theory (RMT) has emerged as a potent framework to characterise the statistical properties of eigenvalues in large complex systems, bridging disciplines from quantum physics to number ...

Scientists analyzed each element of the neutrino mass matrix belonging to leptons and showed theoretically that the intergenerational mixing of lepton flavors is large. Furthermore, by using the ...

We place ourselves in the setting of high-dimensional statistical inference where the number of variables p in a dataset of interest is of the same order of magnitude as the number of observations n.

Random matrices with prescribed eigenvalues and expectation values for random quantum states (with E. Meckes). arXiv A sharp rate of convergence for the empirical spectral measure of a random unitary ...

Jointly funded by the Clay Mathematics Institute and the Heilbronn Institute for Mathematical Research. Influential conjectures from quantum chaos state that the spectral properties of chaotic systems ...

We show that finite-rank perturbations of certain random matrices fit in the framework of infinitesimal (type-B) asymptotic freeness. This can be used to explain the appearance of free harmonic ...

Mark Buchanan’s otherwise admirable piece on random matrices (10 April, p 28) failed to cite the remarkable Tracy-Widom distributions, which, when applied to a given random matrix, will give the ...

When any matter is divided into smaller and smaller pieces, eventually all you are left with—when it cannot be divided any further—is a particle. Currently, there are 12 different known elementary ...