Related papers: Independence relations for exponential fields

A new seemingly weak axiomatic formulation of information algebras is given. It is shown how such information algebras can be embedded into set (information) algebras. In set algebras there is a natural relation of conditional independence…

We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…

The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…

An important dividing line in the class of unstable theories is being NSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking independence may not be as well-behaved as in stable or simple theories, so it is replaced…

In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…

We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable…

This paper introduces new notions of Fubini independence and Exponential independence of random variables under capacities to fit Ellsberg's model, and finds out the relations between Fubini independence, Exponential independence,…

We continue the study of $n$-dependent groups, fields and related structures, largely motivated by the conjecture that every $n$-dependent field is dependent. We provide evidence towards this conjecture by showing that every infinite…

Let E/Q be an elliptic curve with a fixed modular parametrization F : X_0(N) --> E and let P_1,...,P_r be Heegner points on E attached to the rings of integers of distinct quadratic imaginary field k_1,...,k_r. We prove that if the odd…

Eigenfunctions and eigenvalues of the free magnetic Schr\"odinger operator, describing a spinless particle confined to an infinite layer of fixed width, are discussed in detail. The eigenfunctions are realized as an orthonormal basis of a…

We develop some model theory of multi-linear forms, generalizing Granger in the bi-linear case. In particular, after proving a quantifier elimination result, we show that for an NIP field K, the theory of infinite dimensional non-degenerate…

Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for $N$-fermion $d$-dimensional systems. The contributions of both spatial and spin degrees of freedom…

We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…

The method of imsets, introduced by Studen\'y, provides a geometric and combinatorial description of conditional independence statements. Elementary conditional independence statements over a finite set of discrete random variables…

We investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there…

A rational probability distribution on four binary random variables $X, Y, Z, U$ is constructed which satisfies the conditional independence relations $[X \mathrel{\text{$\perp\mkern-10mu\perp$}} Y]$, $[X…

Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…

First, an example of a 2-dependent group without a minimal subgroup of bounded index is given. Second, all infinite n-dependent fields are shown to be Artin-Schreier closed. Furthermore, the theory of any non separably closed PAC field has…

Nesterenko proved, among other results, the algebraic independence over $\QQ$ of the numbers $\pi,e^{\pi},\Gamma(1/4)$. A very important feature of his proof is a multiplicity estimate for quasi-modular forms associated to $\SL_2(\ZZ)$…