From the 1 of 19 linked papers with an AI index.
19 papers
Weak local law and delocalization for the Sachdev-Ye-Kitaev model
Lucas Benigni, Giorgio Cipolloni
We establish a weak mesoscopic local law and quantitative eigenvector-delocalization estimates for the SYK Hamiltonian. For even , we prove that the normalize…
On a Rosenzweig-Porter-type model
Giorgio Cipolloni, László ErdÅs, Joscha Henheik
The paper analyzes a general Rosenzweig‑Porter random matrix model, studying how eigenvector localization and the eigenstate thermalisation hypothesis evolve as the coupling streng…
Gaussian Multiplicative Chaos for i.i.d. matrices
Giorgio Cipolloni, Benjamin Landon
We consider matrices with i.i.d. entries, and prove that the random measure $μ_N(z):=\frac{ | \det (X-z)|^γ}{\mathbb{E}[ | \det (X-z)|^γ]} \mathrm{d} z\mathrm{d} \o…
Sobolev convergence of log-determinants for smooth Wigner matrices
Giorgio Cipolloni, Patrick Lopatto
We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically corre…
The non-Hermitian minor process
Giorgio Cipolloni, László ErdÅs, Oleksii Kolupaiev
We show that the log-determinant of leading principal minors of large non-Hermitian random matrices converges in distribution to a 2+1 dimensional Gaussian field, which is logarith…
Eigenvector decorrelation for random matrices
Giorgio Cipolloni, László ErdÅs, Joscha Henheik +1
We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two defo…