649 citations · 2.6k across the 83 of their papers we have counts for
18 papers · 1 filter
Norm of matrix-valued polynomials in random unitaries and permutations
Charles Bordenave, Benoit Collins
We consider a non-commutative polynomial in several independent -dimensional random unitary matrices, uniformly distributed over the unitary, orthogonal or symmetric groups, and…
On spectral distribution of sample covariance matrices from large dimensional and large -fold tensor products
Benoît Collins, Jianfeng Yao, Wangjun Yuan
We study the eigenvalue distributions for sums of independent rank-one -fold tensor products of large -dimensional vectors. Previous results in the literature assume that $k=…
Strong asymptotic freeness for independent uniform variables on compact groups associated to non-trivial representations
Charles Bordenave, Benoit Collins
Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of rand…
On the operator norm of non-commutative polynomials in deterministic matrices and iid GUE matrices
Benoît Collins, Alice Guionnet, Félix Parraud
Let be a d-tuple of independent GUE random matrices and be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\otime…
Asymptotic Freeness of Unitary Matrices in Tensor Product Spaces for Invariant States
Benoît Collins, Pierre Yves Gaudreau Lamarre, Camille Male
In this paper, we pursue our study of asymptotic properties of families of random matrices that have a tensor structure. In previous work, the first- and second-named authors provi…
Gelfand-Tsetlin polytopes and random contractions away from the limiting shapes
Benoit Collins, Anthony Metcalfe
In this paper, we consider a sequence of selfadjoint matrices having a limiting spectral distribution as , and we consider a sequence of full flags $\{0\le p_1^n…