Related papers: Third Order Cumulants of products
Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…
Many kinds of independence have been defined in non-commutative probability theory. Natural independence is an important class of independence; this class consists of five independences (tensor, free, Boolean, monotone and anti-monotone…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
In this paper we complement our recent result on the explicit formula for the planar limit of the free energy of the two-matrix model by computing the second and third order observables of the model in terms of canonical structures of the…
We develop an entanglement criterion with third- and fourth-order cumulants to detect the entanglement of non-Gaussian states. The efficiency of the entanglement criterion is investigated for gravitating mirrors in optomechanical systems.…
In an earlier version of this paper \cite{6} a formula for the 4th cumulant of the Rosenblatt distribution was derived. In this paper formulas for the 3rd, 4th and 5th cumulant are derived using two methods. In the first method the…
The q-semicircular distribution is a probability law that interpolates between the Gaussian law and the semicircular law. There is a combinatorial interpretation of its moments in terms of matchings where q follows the number of crossings,…
We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the…
We give a nonrecursive, combinatorial characterization of multiplicity-free products of Grassmannian Schubert classes. This answers a question of W. Fulton and extends results of J. Stembridge.
Free cumulants were introduced as the proper analog of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of…
We prove a reciprocity formula between Gauss sums that is used in the computation of certain quantum invariants of 3-manifolds. Our proof uses the discriminant construction applied to the tensor product of lattices.
We present a Hilbert space approach to the limit joint *-distributions of complex independent Gaussian random matrices. For that purpose, we use a suitably defined family of creation and annihilation operators living in some direct integral…
This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.
This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part III), we introduce and study…
The Ginibre ensemble of complex random matrices is studied. The complex valued random variable of second difference of complex energy levels is defined. For the N=3 dimensional ensemble are calculated distributions of second difference, of…
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 derive a formula for the moments and the free cumulants of the multiplication of $k$ free random variables in terms of $k$-equal and $k$-divisible non-crossing partitions. This leads to a new simple proof for the bounds of the right-edge…
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of…
According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula…
Free cumulants are multilinear functionals defined in terms of the moment functional with the use of the family of lattices of noncrossing partitions. In the univariate case, they can be identified with the coefficients of the Voiculescu…