Related papers: Tail algebras of quantum exchangeable random varia…

A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear. Difficulties arising…

As an analogue of the topological boundary of discrete groups $\Gamma$, we define the noncommutative topological boundary of tracial von Neumann algebras $(M, \tau)$ and apply it to generalize the main results of [AHO23], showing that for a…

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a…

We establish Hoeffding-type concentration inequalities for the low and high tail bounds of sums of exchangeable random variables. Our results exhibit an anti-symmetry in such tail bounds due to the assumption of exchangeability, a…

In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…

Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy…

We introduce the notion of Zimmer amenability for actions of discrete quantum groups on von Neumann algebras. We prove generalizations of several fundamental results of the theory in the noncommutative case. In particular, we give a…

In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled…

We clarify the meaning of diagonalizability of quantum Markov states. Then, we prove that each non homogeneous quantum Markov state is diagonalizable. Namely, for each Markov state $\phi$ on the spin algebra $A:={\bar{\otimes_{j\in…

The notion of commutativity of two normal states on a von Neumann algebra was defined some time ago by means of the Pedersen-Takesaki theorem. In this note we aim at generalizing this notion to an arbitrary number of states, and obtaining…

We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate…

We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…

We investigate a construction which associates a finite von Neumann algebra $M(\Gamma,\mu)$ to a finite weighted graph $(\Gamma,\mu)$. Pleasantly, but not surprisingly, the von Neumann algebra associated to to a `flower with $n$ petals' is…

Let $(M, \varphi) = (M_1, \varphi_1) \ast (M_2, \varphi_2)$ be the free product of any $\sigma$-finite von Neumann algebras endowed with any faithful normal states. We show that whenever $Q \subset M$ is a von Neumann subalgebra with…

We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the centered independent ones.

We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group…

In this paper we prove the tail variational principle for actions of countable amenable groups. This allows us to extend some characterizations of asymptotic $h$-expansiveness from $\mathbb{Z}$-actions to actions of countable amenable…

We give a description of operator algebras of free wreath products in terms of fundamental algebras of graphs of operator algebras as well as an explicit formula for the Haar state. This allows us to deduce stability properties for certain…

We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to…

We show that any free product of finite-dimensional von Neumann algebras equipped with non-tracial states is isomorphic to a free Araki-Woods factor with its free quasi-free state possibly direct sum a finite-dimensional von Neumann…