相关论文: Tensor free probability theory: asymptotic tensor …

We obtain a non-asymptotic bound for the expected injective norm of a random tensor with independent entries. This bound is similar to the bound by Bandeira and van Handel (2016) for the expected spectral norm of a random matrix with…

We introduce a new kind of free independence, called real infinitesimal freeness. We show that independent orthogonally invariant with infinitesimal laws are asymptotically real infinitesimally free. We introduce new cumulants, called real…

We prove a central limit theorem for smooth linear statistics related to the zero divisors of Gaussian i.i.d. centered holomorphic sections of tensor powers of a Hermitian holomorphic line bundle over a non-compact Hermitian manifold.

We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…

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…

Let A_1,A_2,...,A_s be a finite sequence of (not necessarily disjoint, or even distinct) non-empty sets of positive integers satisfying a certain condition. It is shown that an independent family U_1,U_2,...,U_s of random NxN permutation…

We consider operator-valued polynomials in Gaussian Unitary Ensemble random matrices and we show that its $L^p$-norm can be upper bounded, up to an asymptotically small error, by the operator norm of the same polynomial evaluated in free…

Random tensors can be used to produce random matrices. This idea is, for instance, very natural when one studies random quantum states with the aim of exploring properties that are generically true, or true with some probability. We hereby…

Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…

We reduce the conditionally monotone (c-monotone) independence of Hasebe to tensor independence. For that purpose, we use the approach developed for the reduction of boolean, free and monotone independences to tensor independence. We apply…

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

We study the joint distribution of the input sum and the output sum of a deterministic transducer. Here, the input of this finite-state machine is a uniformly distributed random sequence. We give a simple combinatorial characterization of…

The Chernoff bound is an important inequality relation in probability theory. The original version of the Chernoff bound is to give an exponential decreasing bound on the tail distribution of sums of independent random variables. Recent…

We show that the limit laws of random matrices, whose entries are conditionally independent operator valued random variables having equal second moments proportional to the size of the matrices, are operator valued semicircular laws.…

We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of "influence" functions of individual random elements described by…

We characterize the limiting second order distributions of certain independent complex Wigner and deterministic matrices using Voiculescu's notions of freeness over the diagonal. If the Wigner matrices are Gaussian, Mingo and Speicher's…

It is shown that a Wishart matrix of standard complex normal random variables is asymptotically freely independent of an independent random matrix, under minimal conditions, in two different sense of asymptotic free independence.

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…

In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for non-commutative random variables. These notions are related to the liberation process introduced by D.…