Related papers: Operators related to subordination for free multip…
In this article, the notion of bi-monotonic independence is introduced as an extension of monotonic independence to the two-faced framework for a family of pairs of algebras in a non-commutative space. The associated cumulants are defined…
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs we derive a new variational formula…
An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory.
Consider the $\mathcal{B}$-valued probability space $(\mathcal{A}, E, \mathcal{B})$, where $\mathcal{A}$ is a tracial von Neumann algebra. We extend the theory of operator valued free probability to the algebra of affiliated operators…
This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
We present a genus expansion-type expression for the expected values of products of traces of expressions involving Haar-distributed orthogonal matrices. As with other real genus expansions, nonorientable surfaces appear, in addition to the…
In this article, by making use of the linear operator introduced and studied by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible functions are investigated and the dual properties of the third-order differential…
The class of subarrangements of the well-studied braid arrangement, so-called graphic hyperplane arrangements, is important for analysing new concepts and properties in hyperplane arrangement theory. While there is a nice characterization…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
We provide a categorical framework for mathematical objects for which there is both a sort of "independent" and "dependent" composition. Namely we model them as duoidal categories in which both monoidal structures share a unit and the first…
We study the multiplicative convolution for c-monotone independence. This convolution unifies the monotone, Boolean and orthogonal multiplicative convolutions. We characterize convolution semigroups for the c-monotone multiplicative…
We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…
Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…
Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a…
This paper provides a compact method to lift the free exponential construction of Mellies-Tabareau-Tasson over the Hyland-Schalk double glueing for orthogonality categories. A condition ``reciprocity of orthogonality'' is presented simply…
We present examples and diagrams illustrating the proofs appearing in "Real second-order freeness and the asymptotic real second-order freeness of several real matrix models", to which this paper is meant to be an appendix. We show how…
We give a construction of two-sided invariant metrics on free products (possibly with amalgamation) of groups with two-sided invariant metrics and, under certain conditions, on HNN extensions of such groups. Our approach is similar to the…
We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one…