59 citations · 106 across the 16 of their papers we have counts for
17 papers
On stability of outliers from the circular law
Guillaume Dubach, Aniss Fares, Lilou Thomas
This work investigates the stability of outliers from the circular law, via the convergence of their associated diagonal overlaps between eigenvectors - also known as the squared e…
On a random matrix proof of a bipartite Harer-Zagier formula
Guillaume Dubach, Hai An Mai
This work establishes a bipartite generalization of the Harer-Zagier formula using non-Hermitian Random Matrix Theory. More specifically, we use a decomposition of powers of Ginibr…
The delocalization of eigenvectors of real elliptic matrices
Lucas Benigni, Simon Coste, Guillaume Dubach
We investigate delocalization phenomena for eigenvectors of real random matrices that are invariant by orthogonal transformations. A specific phenomenon with these ensembles is tha…
Fisher-Hartwig asymptotics for non-Hermitian random matrices
Paul Bourgade, Guillaume Dubach, Lisa Hartung +1
We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to ran…
Dynamics of a rank-one multiplicative perturbation of a unitary matrix
Guillaume Dubach, Jana Reker
We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that b…
On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model
Guillaume Dubach, Pierre Germain, Benjamin Harrop-Griffiths
We consider a nonlinear system of ODEs, where the underlying linear dynamics are determined by a Hermitian random matrix ensemble. We prove that the leading order dynamics in the w…
On the number of cycles in commutators of random permutations
Guillaume Dubach
We present general links between statistics of non-Hermitian random matrices and the distribution of the number of cycles of some specific random permutations. In particular, we de…
Explicit formulas concerning eigenvectors of weakly non-unitary matrices
Guillaume Dubach
We investigate eigenvector statistics of the Truncated Unitary ensemble in the weakly non-unitary case , that is when only one row and column are removed.…
Characteristic polynomials of random truncations: moments, duality and asymptotics
Alexander Serebryakov, Nick Simm, Guillaume Dubach
We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calcu…
Dynamics of a rank-one perturbation of a Hermitian matrix
Guillaume Dubach, László Erdős
We study the eigenvalue trajectories of a time dependent matrix for , where is an Hermitian random matrix and is a unit vector. I…
Formal verification of Zagier's one-sentence proof
Guillaume Dubach, Fabian Muehlboeck
We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier…
Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length
Louis-Pierre Arguin, Guillaume Dubach, Lisa Hartung
We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length , where is either fixed or tends to zero at a s…
On eigenvector statistics in the spherical and truncated unitary ensembles
Guillaume Dubach
We study the overlaps between right and left eigenvectors for random matrices of the spherical and truncated unitary ensembles. Conditionally on all eigenvalues, diagonal overlaps…
On Words of non-Hermitian Random Matrices
Guillaume Dubach, Yuval Peled
We consider words involving i.i.d. complex Ginibre matrices, and study tracial expressions of their eigenvalues and singular values. We show that the limit…
Symmetries of the Quaternionic Ginibre Ensemble
Guillaume Dubach
We establish a few properties of eigenvalues and eigenvectors of the quaternionic Ginibre ensemble (QGE), analogous to what is known in the complex Ginibre case. We first recover a…
The distribution of overlaps between eigenvectors of Ginibre matrices
Paul Bourgade, Guillaume Dubach
We study the overlaps between eigenvectors of nonnormal matrices. They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dy…
Powers of Ginibre Eigenvalues
Guillaume Dubach
We study the images of the complex Ginibre eigenvalues under the power maps , for any integer . We establish the following equality in distribution, $$ {\rm{…