28 citations · 92 across the 10 of their papers we have counts for
12 papers · 1 filter
Local law and delocalization for the Sachdev-Ye-Kitaev model
Lucas Benigni, Giorgio Cipolloni
We establish a mesoscopic local law and quantitative eigenvector-delocalization estimates for the Sachdev--Ye--Kitaev model (SYK) Hamiltonian of interacting Majorana fermions s…
Quantitative eigenvector universality for generalized Wigner matrices
Lucas Benigni, Patrick Lopatto
We present a novel approach to eigenvector universality for generalized Wigner matrices. Our main consequences are asymptotic normality of joint eigenvector projections everywhere…
Fluctuations in Quantum Unique Ergodicity at the Spectral Edge
Lucas Benigni, Nixia Chen, Patrick Lopatto +1
We study the eigenvector mass distribution of an Wigner matrix on a set of coordinates satisfying for some constant . For eigenvectors corresp…
Fluctuations of eigenvector overlaps and the Berry conjecture for Wigner matrices
Lucas Benigni, Giorgio Cipolloni
We prove that any finite collection of quadratic forms (overlaps) of general deterministic matrices and eigenvectors of an Wigner matrix has joint Gaussian fluctuations…
Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks
Lucas Benigni, Sandrine Péché
This paper is concerned with the asymptotic distribution of the largest eigenvalues for some nonlinear random matrix ensemble stemming from the study of neural networks. More preci…
Determinantal structures for Bessel fields
Lucas Benigni, Pei-Ken Hung, Xuan Wu
A Bessel field is a two-variable random field such that for every , has the law of a…
Fluctuations in local quantum unique ergodicity for generalized Wigner matrices
Lucas Benigni, Patrick Lopatto
We study the eigenvector mass distribution for generalized Wigner matrices on a set of coordinates , where , and prove it converg…
Optimal Delocalization for Generalized Wigner Matrices
Lucas Benigni, Patrick Lopatto
We study the eigenvectors of generalized Wigner matrices with subexponential entries and prove that they delocalize at the optimal rate with overwhelming probability. We also prove…
Fermionic eigenvector moment flow
Lucas Benigni
We exhibit new functions of the eigenvectors of the Dyson Brownian motion which follow an equation similar to the Bourgade-Yau eigenvector moment flow. These observables can be see…
Eigenvalue distribution of nonlinear models of random matrices
Lucas Benigni, Sandrine Péché
This paper is concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider with $Y=f(WX)…
Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices
Lucas Benigni
We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N…
Hausdorff Dimension of the Record Set of a Fractional Brownian Motion
Lucas Benigni, Clément Cosco, Assaf Shapira +1
We prove that the Hausdorff dimension of the record set of a fractional Brownian motion with Hurst parameter equals .