Related papers: Note on the Theory of Correlation Functions
We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always…
The computation of the correlation numbers in Minimal Liouville Gravity involves an integration over moduli spaces of complex curves. There are two independent approaches to the calculation: the direct one, based on the CFT methods and…
An infinite set of operator-valued relations in Liouville field theory is established. These relations are enumerated by a pair of positive integers $(m,n)$, the first $(1,1)$ representative being the usual Liouville equation of motion. The…
Inequalities, asymptotics and, for some specific cases, asymptotical expansions were obtained for generalized Mathieu's series. A connection between inequalities for Mathieu's series and positive definite and completely monotonic functions.
The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the U*. The significant relationships and relevance with other results are also given. A number of known univalent conditions…
We survey recent results beyond equidistribution of sequences modulo one. We focus on the sequence of angles in a Euclidean lattice in $\mathbb R^2$ and on the sequence $\sqrt n\bmod1 $.
We study the c_L=25 limit, which corresponds to c=1 string theory, of bulk and boundary correlation functions of Liouville theory with FZZT boundary conditions. This limit is singular and requires a renormalization of vertex operators. We…
We present a theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system. Such higher-order correlation functions have attracted much interest recently in the…
Equations for correlation functions, here referred to as Reynolds- Kraichnan-Lewis equations (RKLE), are considered and their wide application is indicated. Perturbation and non-perturbation solutions are given. To elucidate a closure…
A relationship between partial derivatives of the associated Legendre function of the first kind with respect to its degree, $[\partial P_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$, and to its order, $[\partial P_{n}^{\mu}(z)/\partial\mu]_{\mu=m}$,…
The Uniform convergence of double Fourier-Legendre series of function of bounded Harmonic variation and bounded partial $\Lambda $-variation are investigated.
We study a generalized functional related to the pullback metrics (3). We derive the first variation formula which yield stationary maps. We introduce the stress-energy tensor which is naturally linked to conservation law and yield…
Starting from the known expression for the three-point correlation functions for Liouville exponentials with generic real coefficients at we can prove the Liouville equation of motion at the level of three-point functions. Based on the…
The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula C. We start establishing relationships in the bivariate and…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
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…
We discuss the behavior of harmonic functions on Riemannian cones as defined below and Lioville's theorem.
To illustrate that the notion of convergence of submodular function sequences fits reasonably into the limit theory of graphs, we describe several classes of matroids and other submodular setfunctions for which convergence of appropriate…
Based on new explicit estimates for the prime counting function, we improve the currently known estimates for the particular sequence $C_n = np_n - \sum_{k \leq n}p_k$, $n \geq 1$, involving the prime numbers.
A correlation function of the classical orthogonal polynomials is defined and determined. The correlation function obeys a second order difference equation in two variables. The correlation function for the Gegenbauer, Chebyshev and…