Related papers: On Kim-Independence

Consequences of large $N$ volume independence are examined in conformal and confining gauge theories. In the large $N$ limit, gauge theories compactified on $\R^{d-k} \times (S^1)^k$ are independent of the $S^1$ radii, provided the theory…

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…

We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…

We show how to reduce free independence to tensor independence in the strong sense. We construct a suitable unital *-algebra of closed operators `affiliated' with a given unital *-algebra and call the associated closure `monotone'. Then we…

We develop a theory for state-based noninterference in a setting where different security policies---we call them local policies---apply in different parts of a given system. Our theory comprises appropriate security definitions,…

We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these…

This work investigates the implications of relaxing the measurement independence assumption in Bell's theorem by introducing a new class of local deterministic models that account for both particle preparation and measurement settings. Our…

We prove Kim's Assumtion A for the split classical groups in positive characteristic. Actually, we work in the slightly more general setting of groups of classical kind, which includes quasi-split classical groups and generalized spinor…

Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to…

We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…

We introduce the concept of mutual independence -- correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key -- it is a fully quantum and more…

We give a classification and overview of the confining N=1 supersymmetric gauge theories. For simplicity we consider only theories based on simple gauge groups and no tree-level superpotential. Classification of these theories can be done…

Let $M$ be a module over a Noetherian local ring $A$. We study $M$-independent sequences of elements of $\mathfrak{m}_A$ in the sense of Lech and Hanes. The main tool is a new characterization of the $M$-independence of a sequence in terms…

Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…

We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…

We prove Freudenburg's Freeness Conjecture: Let B be the polynomial ring in three variables over a field of characteristic zero, let D : B --> B be a nonzero locally nilpotent derivation, and let A = ker(D). Then B is a free A-module, and…

We study general quantum integrable Hamiltonians linear in a coupling constant and represented by finite NxN real symmetric matrices. The restriction on the coupling dependence leads to a natural notion of nontrivial integrals of motion and…

We construct a simple, separable, unital, and nuclear C*-algebra with weakly unperforated K_0-group which does not absorb the Jiang-Su algebra Z tensorially. As a result, we obtain a stably finite counter-example to Elliott's classification…

We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…