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 ...

Random matrix theory (RMT) has emerged as a powerful framework for analysing complex systems across physics, statistics and beyond, by examining the statistical properties of matrices with random ...

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 show that, for an n × n random matrix A with independent uniformly anticoncentrated entries such that E ‖ A ‖ HS 2 ≤k n 2 , the smallest singular value σn(A) of A satisfies ℙ{ σ n ( A )≤ ε n }≤Cε+2 ...

In a study published in Physical Review Letters, physicists have demonstrated that black holes satisfy the third law of thermodynamics, which states that entropy remains positive and vanishes at ...

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 ...

A matrix is a rectangular array of numbers. A random matrix can be compared to a Sudoku filled with random numbers. Matrices are part of the equations governing the movements of the particles. In a ...

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 ...