Related papers: How to determine the branch points of correlation …
We compute the two-point correlation function for spin configurations which are obtained by solving the Euclidean matching problem, for one family of points on a grid, and the second family chosen uniformly at random, when the cost depends…
Two-point correlation functions (2PCF) are widely used to characterize how points cluster in space. In this work, we study the problem of measuring the 2PCF over a large set of points, restricted to a subset satisfying a property of…
Motivated by the results presented in a companion paper, here we give a simple analytical expression for the matter n-point functions in the Zel'dovich approximation (ZA) both in real and in redshift space (including the angular case). We…
The highly nonlinear regime of gravitational clustering is characterized by the presence of scale-invariant form of many-body correlation functions. Useful insights can be obtained by investigating the consequences of a generic scaling {\em…
We show that local correlators in a wide class of kicked chains can be calculated exactly at light cone edges. Extending previous works on dual-unitary systems, the correlators between local operators are expressed through the expectation…
The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…
The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a…
We introduce a two-particle correlation function (2PCF) for the Milky Way, constructed to probe spatial correlations in the orthogonal directions of the stellar disk in the Galactic cylindrical coordinates of $R$, $\phi$, and $z$. We use…
The perturbative Chern-Simons theory for knots in Euclidean space is a linear combination of integrals on configuration spaces. This has been successively studied by Bott and Taubes, Altschuler and Freidel, and Yang. We study it again in…
We study the structure of the branch set of solutions to Plateau's problem in metric spaces satisfying a quadratic isoperimetric inequality. In our first result, we give examples of spaces with isoperimetric constant arbitrarily close to…
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions…
(abridged) The large-scale distribution of galaxies is generally analyzed using the two-point correlation function. However, this statistic does not capture the topology of the distribution, and it is necessary to resort to higher order…
Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble Volume simulation cluster…
General results on convex bodies are reviewed and used to derive an exact closed-form parametric formula for the Minkowski sum boundary of $m$ arbitrary ellipsoids in $N$-dimensional Euclidean space. Expressions for the principal curvatures…
We give an Eynard-Orantin type topological recursion formula for the canonical Euclidean volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion comes from the edge removal operation on the space of ribbon…
In this work we perform a systematic study of the singularity structure of inflationary correlations at 1-loop. We explicitly compute a few diagrams and find a pattern emerging in the singularities produced. Motivated by this, we derive…
The Polynomial Freiman-Ruzsa conjecture is one of the central open problems in additive combinatorics. If true, it would give tight quantitative bounds relating combinatorial and algebraic notions of approximate subgroups. In this note, we…
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one…
Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter sigma) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and…
We present an analytic study of conformal field theories on the real projective space $\mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions…