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 ...

We study sample covariance matrices of the form $W=(1/n)CC^{\intercal}$, where C is a k × n matrix with independent and identically distributed (i.i.d.) mean 0 ...

We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance model with divergent spiked eigenvalues, ...

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 ...

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 ...

M. Stolz, Ensembles of Hermitian random matrices associated to symmetric spaces, in: J. Hilgert et al. (eds.), Infinite Dimensional Harmonic Analysis IV. On the Interplay between Representation Theory ...

Scientists are exploring a mysterious pattern, found in birds’ eyes, boxes of marbles and other surprising places, that is neither regular nor random. All complex correlated systems, from Arctic melt ...

Harry Markowitz famously quipped that diversification is the only free lunch in investing. What he did not say is that this is only true if correlations are known and stable over time. Markowitz’s ...

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 ...