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We introduce nonparametric tests of independence for bivariate circular data based on trigonometric moments. Our contributions lie in (i) proposing nonparametric tests that are locally and asymptotically optimal against bivariate cosine von…
This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability…
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 study pairs of reals that are mutually Martin-L\"{o}f random with respect to a common, not necessarily computable probability measure. We show that a generalized version of van Lambalgen's Theorem holds for non-computable probability…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
In this paper, we characterize several classes of continuous radial basis functions that can be employed to determine whether a interaction of a probability is zero or not. These functions encompass standard independence tests but also the…
Various versions of "independence" are actively inverstigated in quantum probability. In the context of relativistic QFT, we show here that the physical origin of "independence" can be sought in the asymptotic condition through which…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
In this paper, an analogue of matrix models from free probability is developed in the bi-free setting. A bi-matrix model is not simply a pair of matrix models, but a pair of matrix models where one element in the pair acts by…
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…
Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…
We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive…
Non-commutative versions of Arveson's curvature invariant and Euler characteristic for a commuting $n$-tuple of operators are introduced. The non-commutative curvature invariant is sensitive enough to determine if an $n$-tuple is free. In…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
For a family of unital free *-algebras with a family of states on them, we construct a sequence of noncommutative probability spaces, which are tensor product algebras with tensor product states and which approximate the free product of…
A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur…
The algebra Mul[[B]] of formal multilinear function series over an algebra B and its quotient SymMul[[B]] are introduced, as well as corresponding operations of formal composition. In the setting of Mul[[B]], the unsymmetrized R- and…
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
The wrapping transformation $W$ is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measures on the circle, with the multiplicative convolution…
We construct several new spaces of quantum sequences and their quantum families of maps in sense of So{\l}tan. Then, we introduce noncommutative distributional symmetries associated with these quantum maps and study simple relations between…