Core Concepts
The local eigenvalue statistics at cusp singularities of correlated random matrices are universal, proven using the Zigzag strategy, a novel method that simplifies the proof and avoids previous technical obstacles.
Quotes
"The celebrated Wigner-Dyson-Mehta (WDM) conjecture asserts that the local eigenvalue statistics of large random matrices become universal: they depend only on the symmetry class of the matrix and not on the precise details of its distribution."
"The third and final class of universal local statistics emerges at the cusp-like singularities of the density with cubic-root behavior."
"Our main result fills this gap by proving the universality of the local eigenvalues statistics at the cusp for random matrices with correlated entries and an arbitrary deformation."
"In this paper, we leverage the Zigzag strategy to conveniently avoid the complicated graphical expansions and, more importantly, circumvent the extraction of σ-cells."