Related papers: Matrix liberation process II: Relation to orbital …
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the…
We present here some connections between the liberation process for projections $(P,Q)\mapsto(P,U_tQU_t^*)$ and its counterpart $(R,S)\mapsto(R,U_tSU_t^*)$ for symmetries when the projections $\{P,Q\}$ and the symmetries $\{R,S\}$ are…
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…
I consider multipartite processes in which there are constraints on each subsystem's rate matrix, restricting which other subsystems can directly affect its dynamics. I derive a strictly nonzero lower bound on the minimal achievable entropy…
We use techniques from finite free probability to analyze matrix processes related to eigenvalues, singular values, and generalized singular values of random matrices. The models we use are quite basic and the analysis consists entirely of…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
The partial transposition from quantum information theory provides a new source to distill the so-called asymptotic freeness without the assumption of classical independence between random matrices. Indeed, a recent paper [MP19] established…
We investigate the average entropy of a subsystem within a global unitary orbit of a given mixed bipartite state in the finite-dimensional space. Without working out the closed-form expression of such average entropy for the mixed state…
We prove that the quantum relative entropy is a rate function in large deviation principle. Next, we define information criteria for quantum states and estimate the accuracy of the use of them. Most of the results in this paper are…
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…
We show that finite rank perturbations of certain random matrices fit in the framework of infinitesimal (type B) asymptotic freeness. This can be used to explain the appearance of free harmonic analysis (such as subordination functions…
Using new combinatorial techniques, we significantly improve the previous results on asymptotic distributions and asymptotic free independence relations of partial transposes of Wishart random matrices. In particular, we give a necessary…
The excess work required to drive a stochastic system out of thermodynamic equilibrium through a time-dependent external perturbation is directly related to the amount of entropy produced during the driving process, allowing excess work and…
In this paper we address the problem of systems under an external feedback. This is performed using a large deviation approach and rate distortion from information theory. In particular we define a lower boundary for the maximum entropy…
This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…
A lower estimate of the orbital free entropy $\chi_\mathrm{orb}$ under unitary conjugation is proved, and it together with Voiculescu's observation shows that the conjectural exact formula relating $\chi_\mathrm{orb}$ to the free entropy…
There is demand in diverse fields for a reliable method of estimating the entropy associated with correlations. The estimation of a unique entropy directly from the Pearson correlation matrix has remained an open problem for more than half…