Related papers: The Monotone Cumulants
Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
The general methods which are powerful for the necessity of bounded commutators are given. As applications, some necessary conditions for bounded commutators are first obtained in certain endpoint cases, and several new characterizations of…
This paper describes the expected characteristic polynomial of the commutator of randomly rotated matrices, in the context of the finite free probability theory initiated by Marcus, Spielman, and Srivastava. The key technical features are…
A combinatorial proof of the unimodality of the generalized q-Gaussian coefficients based on the explicit formula for Kostka-Foulkes polynomials is given.
In this paper, we introduce a generalized notion of monotone property and prove some results regarding existence and uniqueness of multi-tupled fixed points for nonlinear contraction mappings satisfying monotone property in ordered complete…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular $k$-gons. For $n\le 4$ we determine formulas for the number $a_k(n)$ of generalized polyominoes consisting of $n$ regular $k$-gons.…
In parallel to the classical theory of central extensions of groups, we develop a version for extensions that preserve commutativity. It is shown that the Bogomolov multiplier is a universal object parametrising such extensions of a given…
We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of Banica, Curran and Speicher. We determine maximal…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
Motivated by recent work on mixtures of classical and free probabilities, we introduce and study the notion of $\epsilon$-noncrossing partitions. It is shown that the set of such partitions forms a lattice, which interpolates as a poset…
In this paper we shall prove that any $2$-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary…
We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the…
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…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
In the theory of crossed modules, considering arbitrary self-actions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of generalized crossed module emerges. In this paper we give a…
The extended commutation relations for a generalized uncertainty principle have been based on the assumption of the minimal length in position. Instead of this assumption, we start with a constrained Hamiltonian system described by the…
We prove a formula to express multivariate monotone cumulants of random variables in terms of their moments by using a Hopf algebra of decorated Schr\"oder trees.