Related papers: Power spectrum of the fluctuation of Chebyshev's p…
The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found…
Fluctuations of the electromagnetic field produced by quantized matter in external electric field are investigated. A general expression for the power spectrum of fluctuations is derived within the long-range expansion. It is found that in…
The power spectrum of quantum fluctuations of the electromagnetic field produced by an elementary particle is determined. It is found that in a wide range of practically important frequencies the power spectrum of fluctuations exhibits an…
Fluctuations in the large-scale structure of the Universe contain significant information about cosmological physics, but are modulated in survey datasets by various observational effects. Building on existing literature, we provide a…
We consider a directed abelian sandpile on a strip of size $2\times n$, driven by adding a grain randomly at the left boundary after every $T$ time-steps. We establish the exact equivalence of the problem of mass fluctuations in the steady…
The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a…
We describe an attempt to reconstruct the initial conditions for the formation of cosmological large-scale structure. The power spectrum of the primordial fluctuations is affected by bias, nonlinear evolution and redshift-space distortions,…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…
Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known…
To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By…
We explore power spectrum estimation in the context of a Gaussian approximation to the likelihood function. Using the Saskatoon data, we estimate the power averaged through a set of ten filters designed to make the errors on the power…
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…
We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal in- variance. On the basis of our data sets we…
In this paper we give new estimates for integrals involving some arithmetic functions defined over prime numbers. The main focus here is on the prime counting function $\pi(x)$ and the Chebyshev $\vartheta$-function. Some of these estimates…
We derive power counting formulas for ribbon graph amplitudes that were recently independently discovered in two contexts, namely as a generalization of the Kontsevich model, and as corresponding to a matrix model approach to the spectral…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
The statistical properties of a map of the primary fluctuations in the cosmic microwave background (CMB) may be specified to high accuracy by a few thousand power spectra measurements, provided the fluctuations are gaussian, yet the number…
We calculate the power spectrum of metric fluctuations in inflationary cosmology starting with initial conditions which are imposed mode by mode when the wavelength equals some critical length $\ell_{_{\rm C}}$ corresponding to a new energy…
Accurate estimation of galaxy cluster masses is a central problem in cosmology. Turbulence is believed to introduce significant deviations from the hydrostatic mass estimates. Estimation of turbulence properties is complicated by projection…
In this paper we first establish new explicit estimates for Chebyshev's $\vartheta$-function. Applying these new estimates, we derive new upper and lower bounds for some functions defined over the prime numbers, for instance the prime…