Related papers: Self-Correlation and Maximum Independence in Finit…
When massless particles are involved, the traditional scattering matrix ($S$-matrix) does not exist: it has no rigorous non-perturbative definition and has infrared divergences in its perturbative expansion. The problem can be traced to the…
We investigate the algebra and geometry of the independence conditions on discrete random variables in which we fix some random variables and study the complete independence of some subcollections. We interpret such independence conditions…
We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with…
Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion…
We generalize the single-field consistency relations to capture not only the leading term in the squeezed limit---going as 1/q^3, where q is the small wavevector---but also the subleading one, going as 1/q^2. This term, for an (n+1)-point…
Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. Here we show that such poles can be related to linear branches of…
Configurational polyhedora (CP) is a hyperpolyhedra on multidimensional configuration space, whose vertex (and edges) corresponds to upper or lower limit value of correlation functions for all possible atomic configuration on given lattice.…
We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices.…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
We present a number of results concerning infinite-exponent partition relations on linear orders of the form $\langle {}^\alpha 2,<_{\text{lex}}\rangle$ for $\alpha$ an ordinal, generalising the setting of the real line, working throughout…
This course introduces the fruitful links between model theory and a combinatoric of sets given by independence relations. An independence relation on a set is a ternary relation between subsets. Chapter 1 should be considered as an…
This paper studies the connection between probabilistic conditional independence in uncertain reasoning and data dependency in relational databases. As a demonstration of the usefulness of this preliminary investigation, an alternate proof…
An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
We analyze topological objects in pure gluonic $SU(2)$ lattice gauge theory and compute correlation functions between instantons and monopoles. Concerning the instantons we use geometric and field theoretic definitions of the topological…
For multivariate data, dependence beyond pair-wise can be important. This is true, for example, in using functional MRI (fMRI) data to investigate brain functional connectivity. When one has more than a few variables, however, the number of…
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems,…
We present a large deviations theory of the spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, both at finite and zero temperature. Rare events of atypically correlated variables are particularly important…