Related papers: Mixtures of classical and free independence
We use here a recent idea of studying functions of free random variables using Boolean cumulants. We develop idea of explicit calculations of conditional expectation using Boolean cumulants. We demonstrate Boolean cumulants approach allows…
In a previous paper (called "Rectangular random matrices. Related covolution"), we defined, for $\lambda \in [0,1]$, the rectangular free convolution with ratio $\lambda$. Here, we investigate the related notion of infinite divisiblity,…
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.
We formulate the problem of finding self-dual Hamiltonians (associated with integrable systems) as deformations of free systems given on various symplectic manifolds and discuss several known explicit examples, including recently found…
We develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods. One of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing…
We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to $\varepsilon$-free independence, a mixture of classical and free independence studied by M{\l}otkowski and by Speicher and…
We consider a possibility to describe spin one-half and higher spins of massive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables $x^\mu,\xi_\alpha,\chi_\alpha$, where $\xi,\chi$…
We investigate atomicity of free algebras and various forms of amalgamation for BL and MV algebras, and also Heyting algebras, though the latter algebras may not be linearly ordered, so strictly speaking their corresponding intuitionistic…
We describe an algebra for composing automata which includes both classical and quantum entities and their communications. We illustrate by describing in detail a quantum protocol.
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
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.
The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
Recent developments have found unexpected connections between non-commutative probability theory and algebraic topology. In particular, Boolean cumulants functionals seem to be important for describing morphisms of homotopy operadic…
We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…
Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $\Lambda$ as an independent scalar field, and supplemented by the Euler and…
Let A be a unital $C^*$-algebra, given together with a specified state $\phi:A \to C$. Consider two selfadjoint elements a,b of A, which are free with respect to $\phi$ (in the sense of the free probability theory of Voiculescu). Let us…
Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent…
In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…
Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord…