Related papers: Operator Method and Recursion Relations for Inflat…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
Duality relations are obtained for correlation functions of the q-state Potts model on any planar lattice or graph using a simple graphical analysis. For the two-point correlation we show that the correlation length is precisely the surface…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
A procedure is developed for the recovery of the inflationary potential over the interval that affects astrophysical scales ($\approx 1\Mpc - 10^4\Mpc$). The amplitudes of the scalar and tensor metric perturbations and their power-spectrum…
We extend an earlier, configuration space method to find the Wilson coefficients of operators appearing in the short distance expansion of thermal correlation functions of different quark bilinears. Considering all the different correlation…
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new…
In this paper we survey and bring together several approaches to obtaining inner functions for Toeplitz operators. These approaches include the classical definition, the Wold decomposition, the operator-valued Poisson Integral, and Clark…
We present Monte Carlo reconstruction, a new method for ``inverting'' observational data to constrain the form of the scalar field potential responsible for inflation. This stochastic technique is based on the flow equation formalism and…
We find direct and inverse recursion operators for integrable cases of the rmdKP and rdDym equations. Also, we study actions of these operators on the contact symmetries and find shadows of nonlocal symmetries of these equations.
We construct supergravity models allowing to sequester the phenomenology of inflation from the Planckian energy scale physics. The procedure consists of two steps: At Step I we study supergravity models, which might be associated with…
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…
We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of…
A theory is presented for a novel recursion method for O(N) ab initio tight-binding calculations. A long-standing problem of generalizing the recursion method to a non-orthogonal basis, which is a crucial step to make the recursion method…
In this work, we analyze two possible alternative and model-independent approaches to describe the inflationary period. The first one assumes a general equation of state during inflation due to Mukhanov, while the second one is based on the…
We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to $F$-subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion of "harmonic interpolation" that we…
In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional…
We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…
This study presents a generalization for a method examining the correlation function of an arbitrary system with interactions in an Ising model to obtain a value of correlation between two arbitrary points on a network. The establishment of…
The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…