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In this paper we find necessary and sufficient conditions for the weak convergence of c-free convolution of pairs of measures, where the measures are assumed to be infinitesimal and their support may be unbounded. These results are obtained…
We consider the question of the additivity of strong homology. This entails isolating the set-theoretic content of the higher derived limits of an inverse system indexed by the functions from $\mathbb{N}$ to $\mathbb{N}$. We show that this…
Non-associative algebras appear in some quantum-mechanical systems, for instance if a charged particle in a distribution of magnetic monopoles is considered. Using methods of deformation quantization it is shown here, that algebras for such…
A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we…
The free central-limit theorem, a fundamental theorem in free probability, states that empirical averages of freely independent random variables are asymptotically semi-circular. We extend this theorem to general dynamical systems of…
It is shown that modular invariance provides a natural explanation for the absence of monopoles when assumed to be a discrete gauge symmetry. It follows that monopoles can not be seen because it is always possible to find a suitable…
We give a definition of finitary type theories that subsumes many examples of dependent type theories, such as variants of Martin-L\"of type theory, simple type theories, first-order and higher-order logics, and homotopy type theory. We…
We give an improved estimate for the density of $k$-free values of integral binary forms with no fixed $k$-th power divisor. Further, we give the corresponding improvement to a theorem of Stewart and Top on the number of power-free values…
In this paper we formulate a conjecture which is a strengthening of an extension theorem of Bakonyi and Timotin for positive definite functions on the free group on two generators. We prove that this conjecture implies Connes' embedding…
We consider commutator-free exponential integrators as put forward in [Alverman, A., Fehske, H.: High-order commutator-free exponential time-propagation of driven quantum systems. J. Comput. Phys. 230, 5930-5956 (2011)]. For parabolic…
Bell's theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the…
In this paper, the notion of conditionally bi-free independence for pairs of algebras is introduced. The notion of conditional $(\ell, r)$-cumulants are introduced and it is demonstrated that conditionally bi-free independence is equivalent…
We show the exponential decay of eigenfunctions of second-order geometric many-body type Hamiltonians at non-threshold energies. Moreover, in the case of first order and small second order perturbations we show that there are no…
We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by their inert maps. We show that left Kan extension along the inclusion $j \colon \Delta_{\operatorname{inert}} \to \Delta$ takes general…
Suppose that M is countable, binary, primitive, homogeneous, and simple, and hence 1-based. We prove that the SU-rank of the complete theory of M is~1. It follows that M is a random structure. The conclusion that M is a random structure…
In this note we show that there exist a $2^\mathfrak{c}$-generated free algebra $\mathcal{S} \subset \mathbb{R}^\mathbb{R}$ of Riemann integrable functions and a free algebra $\mathcal{C} \subset \mathbb{R}^{[0,1]}$ of continuous functions,…
We introduce a notion of non-commutative joint independence for multiple algebras in a non-commutative probability space. The pairwise relationships between these algebras are encoded by a graph with two edge sets -- a combinatorial…
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to…
We present a review of the homological algebra tools involved in the standard de Rham theory and their subsequent generalizations relevant for the understanding of free massless higher spin gauge structure. M-theory arguments suggest the…