Related papers: Convergence for noncommutative rational functions …
We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…
Let $a_{1},...,a_{n}, b_{1},...,b_{n}$ be random variables in some (non-commutative) probability space, such that $\{a_{1}, ..., a_{n} \}$ is free from $\{b_{1}, ..., b_{n} \}$. We show how the joint distribution of the $n$-tuple $(a_{1}…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
In random matrix theory, the spacing distribution functions $p^{(n)}(s)$ are well fitted by the Wigner surmise and its generalizations. In this approximation the spacing functions are completely described by the behavior of the exact…
The paper gives analogues of some starting results in the theory of Gaussian Hilbert Spaces for semicircular distributed random variables. The transition from the commutative to the free frame is done considering matrices of increasing…
In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
Finding a good way to model probability densities is key to probabilistic inference. An ideal model should be able to concisely approximate any probability while being also compatible with two main operations: multiplications of two models…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
We address the noncommutative version of the Edmonds' problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algorithm for the calculation of this inner rank by relating the problem with the…
We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
We study the properties of the set of marginal distributions of infinite translation-invariant systems in the 2D square lattice. In cases where the local variables can only take a small number $d$ of possible values, we completely solve the…
We characterize functions of $d$-tuples of bounded operators on a Hilbert space that are uniformly approximable by free polynomials on balanced open sets.
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…