From the 1 of 19 linked papers with an AI index.
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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…
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…
Fluctuations for non-Hermitian dynamics
Paul Bourgade, Giorgio Cipolloni, Jiaoyang Huang
We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinso…