Related papers: Point Processes and the Infinite Symmetric Group. …
We compare two definitions of connected correlation functions in fluctuating geometries. We show results of the MC simulations for 4D dynamical triangulation in the elongated phase and compare them with the exact calculations of correlation…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Let $X$ be a locally compact, second countable Hausdorff topological space. We consider a family of commuting Hermitian operators $a(\Delta)$ indexed by all measurable, relatively compact sets $\Delta$ in $X$ (a quantum stochastic process…
We reduce the computation of three point function of three spinning operators with arbitrary polarizations to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the…
Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of…
We initiate the study of four-point functions of large BPS operators at any value of the coupling. We do it by casting it as a sum over exchange of superconformal primaries and computing the structure constants using integrability. Along…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
We construct a new representation for two- and three-point correlators of operators from sl(2) sector of planar N = 4 SYM. The spin and twist of operators are arbitrary. We start with the correlation function of light-ray operators and…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…
Second-order variational type equations for spatial point processes are established. In case of log linear parametric models for pair correlation functions, it is demonstrated that the variational equations can be applied to construct…
We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss…
Multi-output Gaussian processes (MOGPs) have been introduced to deal with multiple tasks by exploiting the correlations between different outputs. Generally, MOGPs models assume a flat correlation structure between the outputs. However,…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small…
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with…
The n-point correlation functions introduced by Bloch and Okounkov have already found several geometric connections and algebraic generalizations. In this Note we formulate a q,t-deformation of this n-point function. The key operator used…
We investigate proposals of how the form factor approach to compute correlation functions at zero temperature can be extended to finite temperature. For the two-point correlation function we conclude that the suggestion to use the usual…
Many--particle correlations due to Bose-Einstein interference are studied in ultrarelativistic heavy--ion collisions. We calculate the higher order correlation functions from the 2--particle correlation function by assuming that the source…
We extend the theory of topological recursion by considering Airy structures whose partition functions are highest weight vectors of particular $\mathcal{W}$-algebra representations. Such highest weight vectors arise as partition functions…
This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…