Related papers: Large permutation invariant random matrices are as…
We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…
The asymptotic freeness of independent unitarily invariant $N\times N$ random matrices holds in expectation up to $O(N^{-2})$. An already known consequence is the infinitesimal freeness in expectation. We put in evidence another consequence…
We consider (self-adjoint) families of infinite matrices of noncommutative random variables such that the joint distribution of their entries is invariant under conjugation by a free quantum group. For the free orthogonal and…
Applying the concept of matricial freeness which generalizes freeness in free probability, we have recently studied asymptotic joint distributions of symmetric blocks of Gaussian random matrices (Gaussian Symmetric Block Ensemble). This…
Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of random unitaries and strong asymptotic freeness of random…
It has been shown by Voiculescu that important classes of square independent random matrices are asymptotically free, where freeness is a noncommutative analog of classical independence. Recently, we introduced the concept of matricial…
On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of…
For a sufficiently nice 2 dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to a given pattern. For large approximating matrices, we observe that the…
We prove that any non commutative polynomial of r independent copies of Wigner matrices converges a.s. towards the polynomial of r free semicircular variables in operator norm. This result extends a previous work of Haagerup and…
A recent development in random matrix theory, the intrinsic freeness principle, establishes that the spectrum of very general random matrices behaves as that of an associated free operator. This reduces the study of such random matrices to…
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint…
Recent work of Belinschi, Mai and Speicher resulted in a general algorithm to calculate the distribution of any selfadjoint polynomial in free variables. Since many classes of independent random matrices become asymptotically free if the…
In this paper we consider Wigner random matrices -- symmetric n by n random matrices whose entries are independent identically distributed real random variables. We prove that the probability distribution of one or several eigenvalues close…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…
We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show…
We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…
In this work we study symmetric random matrices with variance profile satisfying certain conditions. We establish the convergence of the operator norm of these matrices to the largest element of the support of the limiting empirical…
Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…