Related papers: Higher order relativistic galaxy number counts: do…
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…
The weak gravitational lensing effect, small coherent distortions of galaxy images by means of a gravitational tidal field, can be used to study the relation between the matter and galaxy distribution. In this context, weak lensing has so…
We discuss the first results obtained on the study of a sample of high-z galaxies (2 < z < 7), using the gravitational amplification effect in the core of lensing clusters. Sources are located close to the critical lines in clusters with…
Owing to their more extensive sky coverage and tighter control on systematic errors, future deep weak lensing surveys should provide a better statistical picture of the dark matter clustering beyond the level of the power spectrum. In this…
In this paper we study the hard-thermal-loop effective theory at next-to-leading order. Standard power-counting predicts that a large number of diagrams, including 2-loop diagrams, may need to be calculated. In all of the calculations that…
Quantum tomography, as a tool to probe foundational aspects of quantum mechanics, relies on extracting spin information from angular distributions. This is inherently a leading-order technique, ill-defined when higher-order corrections are…
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
The reconstruction method was proposed more than a decade ago to boost the signal of baryonic acoustic oscillations measured in galaxy redshift surveys, which is one of key probes for dark energy. After moving the observed overdensities in…
We introduce numbers depending on three parameters which we call skyscraper numbers. We discuss properties of these numbers and their relationship with Stirling numbers of the first kind, and we also introduce a skyscraper sequence.
We develop the formalism to include substructure in the halo model of clustering. Real halos are not likely to be perfectly smooth, but have substructure which has so far been neglected in the halo model -- our formalism allows one to…
We consider the problem of reducing a first-order Markov chain on a large alphabet to a higher-order Markov chain on a small alphabet. We present information-theoretic cost functions that are related to predictability and lumpability, show…
In this thesis, I present three projects I carried out during m PhD. In the first project, I introduce Conformal Transformations and the Galaxy Number County. I explicitly show that the Galaxy Number Counts is invariant under Conformal…
The super-horizon second-order density perturbations corresponding to cosmological random fluctuations are considered, their non-vanishing spatial average is shown to be useful in solving the serious problem on the cosmological tension…
In this paper we study the sets of integers which are $n$-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for $n$ sufficiently large. We also develop bounds on the growth…
We show that current surveys have at least as much signal to noise in higher-order statistics as in the power spectrum at weakly nonlinear scales. We discuss how one can use this information to determine the mean of the galaxy halo…
Cosmological analyses of second-order weak lensing statistics require precise and accurate covariance estimates. These covariances are impacted by two sometimes neglected terms: A negative contribution to the Gaussian covariance due to…
The scalar field theory with higher derivatives is considered in the first order formalism. The field equation of the forth order describes scalar particles possessing two mass states. The first order relativistic wave equation in the…
The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…
This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar…
Let G be a semisimple Lie group without compact factors, \Gamma be an irreducible lattice in G. In the first part of the article we give the necessary and sufficient condition under which a sequence of translates of probability…