Related papers: Selfless W$^*$-probability spaces and Connes' bice…

Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for the position and momentum. Most notably, they both give correct one-dimensional marginal probability…

We describe the one-dimensional \v{C}eby\v{s}\"{e}v subspaces of a JBW$^*$-triple $M,$ by showing that for a non-zero element $x$ in $M$, $\mathbb{C}x$ is a \v{C}eby\v{s}\"{e}v subspace of $M$ if, and only if, $x$ is a Brown-Pedersen…

Let $(M, \varphi) = (M_1, \varphi_1) \ast (M_2, \varphi_2)$ be a free product of arbitrary von Neumann algebras endowed with faithful normal states. Assume that the centralizer $M_1^{\varphi_1}$ is diffuse. We first show that any…

The purpose of this paper is to obtain a sufficient and necessary condition as a criteria to test whether an arbitrary multipartite state is entangled or not. Based on the tensor expression of a multipartite pure state, the paper shows that…

We characterize semicircular distribution by the freeness of linear and quadratic forms in noncommutative random variables from a tracial $W^*$-probability space with relaxed moment conditions.

This paper deals with a "naive" way of generalization of the Kazhdan's property (T) to C*-algebras. This approach differs from the approach of Connes and Jones, which has already demonstrated its utility. Nevertheless it turned out that our…

We study a class of inverse monoids of the form M = Inv< X | w=1 >, where the single relator w has a combinatorial property that we call sparse. For a sparse word w, we prove that the word problem for M is decidable. We also show that the…

By the Lindeberg-L\'evy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual…

We show that the conditional independence (CI) implication problem with bounded cardinalities, which asks whether a given CI implication holds for all discrete random variables with given cardinalities, is co-NEXPTIME-hard. The problem…

We present a consistent BPS framework for a generalized Maxwell-Chern-Simons-Higgs model. The overall model, including its self-dual potential, depends on three different functions, h(|{\phi}|,N), w(|{\phi}|) and G(|{\phi}|), which are…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

In this paper we give a proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudo-differential operators is equivalent to condition ($\Psi$). This condition rules out certain sign changes of the imaginary…

We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter $\theta^{\mu\nu}$, with…

The exact dynamics of a disordered spin star system, describing a central spin coupled to N distinguishable and non interacting spins 1/2, is reported. Exploiting their interaction with the central single spin system, we present possible…

In any probabilistic theory, we may say a bipartite state on a composite system AB steers its marginal state (on, say, system B) if, for any decomposition of the marginal as a mixture, with probabilities p_i, of states b_i of B, there…

There is a renewed interest in weak model sets due to their connection to $\mathcal B$-free systems, which emerged from Sarnak's program on the M\"obius disjointness conjecture. Here we continue our recent investigation [arXiv:1511.06137]…

We prove a generalization of the Conley conjecture: Every Hamiltonian diffeomorphism of a closed symplectic manifold has infinitely many periodic orbits if the first Chern class vanishes over the second fundamental group. In particular, we…

The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore,…

We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…