Related papers: Some Bi-Matrix Models for Bi-Free Limit Distributi…
We introduce and study `matricial circular systems' of operators which play the role of matricial counterparts of circular operators. They describe the asymptotic joint *-distributions of blocks of independent block-identically distributed…
In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of…
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…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible…
We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of "second order freeness" and derive the global fluctuations of Gaussian and…
We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called…
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…
In this paper, we construct random two-faced families of matrices with non-Gaussian entries to approximate a two-faced family of random variables having a bi-free central limit distribution. We prove that, under modest conditions weaker…
We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants and the bi-free…
The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…
We introduce real second-order freeness in second-order noncommutative probability spaces. We demonstrate that under this definition, three real models of random matrices, namely real Ginibre matrices, Gaussian orthogonal matrices, and real…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
We study the joint distribution of SYK Hamiltonians for different systems with specified overlaps. We show that, in the large-system limit, their joint distribution converges in distribution to a mixed $q$-Gaussian system. We explain that…
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by…
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…
In this paper, a connection between bi-free probability and the theory of non-commutative stochastic processes is examined. Specifically it is demonstrated that the transition operators for non-commutative stochastic processes can be…
I study the product of independent identically distributed $D\times D$ random probability matrices. Some exact asymptotic results are obtained. I find that both the left and the right products approach exponentially to a probability…
We show that an independent family of uniformly distributed random permutation matrices is asymptotically *-free from an independent family of square complex Gaussian matrices and from an independent family of complex Wishart matrices, and…
The free central-limit theorem, a fundamental theorem in free probability, states that empirical averages of freely independent random variables are asymptotically semi-circular. We extend this theorem to general dynamical systems of…