scholarly journals Non-Gaussian density fluctuations from entropically generated curvature perturbations in ekpyrotic models

2008 ◽  
Vol 77 (6) ◽  
Author(s):  
Jean-Luc Lehners ◽  
Paul J. Steinhardt
Keyword(s):  
Density Fluctuations ◽  
Gaussian Density ◽  
Non Gaussian

scholarly journals Cosmological model parameter dependence of the matter power spectrum covariance from the DEUS-PUR Cosmo simulations

2020 ◽  
Vol 500 (2) ◽  
pp. 2532-2542
Author(s):  
Linda Blot ◽  
Pier-Stefano Corasaniti ◽  
Yann Rasera ◽  
Shankar Agarwal
Keyword(s):  
Dark Energy ◽  
Power Spectrum ◽  
Cold Dark Matter ◽  
Matter Density ◽  
Density Fluctuations ◽  
Matrix Analysis ◽  
Model Parameter ◽  
Matter Power Spectrum ◽  
Non Gaussian ◽  
The Impact

ABSTRACT Future galaxy surveys will provide accurate measurements of the matter power spectrum across an unprecedented range of scales and redshifts. The analysis of these data will require one to accurately model the imprint of non-linearities of the matter density field. In particular, these induce a non-Gaussian contribution to the data covariance that needs to be properly taken into account to realize unbiased cosmological parameter inference analyses. Here, we study the cosmological dependence of the matter power spectrum covariance using a dedicated suite of N-body simulations, the Dark Energy Universe Simulation–Parallel Universe Runs (DEUS-PUR) Cosmo. These consist of 512 realizations for 10 different cosmologies where we vary the matter density Ωm, the amplitude of density fluctuations σ8, the reduced Hubble parameter h, and a constant dark energy equation of state w by approximately $10{{\ \rm per\ cent}}$. We use these data to evaluate the first and second derivatives of the power spectrum covariance with respect to a fiducial Λ-cold dark matter cosmology. We find that the variations can be as large as $150{{\ \rm per\ cent}}$ depending on the scale, redshift, and model parameter considered. By performing a Fisher matrix analysis we explore the impact of different choices in modelling the cosmological dependence of the covariance. Our results suggest that fixing the covariance to a fiducial cosmology can significantly affect the recovered parameter errors and that modelling the cosmological dependence of the variance while keeping the correlation coefficient fixed can alleviate the impact of this effect.

scholarly journals Modelling with star-shaped distributions

2020 ◽  
Vol 8 (1) ◽  
pp. 45-69
Author(s):  
Eckhard Liebscher ◽  
Wolf-Dieter Richter
Keyword(s):  
Probabilistic Models ◽  
Arbitrary Dimension ◽  
Probability Density Functions ◽  
Density Functions ◽  
Wide Range ◽  
Gaussian Density ◽  
Spherical Distributions ◽  
Data Points ◽  
Non Gaussian ◽  
General Method

AbstractWe prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.

M-Ary Alpha-Stable Noise Modulation in Spread-Spectrum Communication

2015 ◽  
Vol 14 (03) ◽  
pp. 1550022 ◽  
Author(s):  
Mehmet Emre Cek
Keyword(s):  
Gaussian Noise ◽  
Spread Spectrum ◽  
Additive White Gaussian Noise ◽  
Characteristic Exponent ◽  
Random Signal ◽  
Spread Spectrum Communication ◽  
Order Moment ◽  
Gaussian Density ◽  
Shift Keying ◽  
Non Gaussian

In this paper, a spread-spectrum communication system based on a random carrier is proposed which transmits M-ary information. The random signal is considered as a single realization of a random process taken from prescribed symmetric α-stable (SαS) distribution that carries digital M-ary information to be transmitted. Considering the noise model in the channel as additive white Gaussian noise (AWGN), the transmitter sends the information carrying random signal from non-Gaussian density. Alpha-stable distribution is used to encode the M-ary message. Inspired by the chaos shift keying techniques, the proposed method is called M-ary symmetric alpha-stable differential shift keying (M-ary SαS-DSK). The main purpose of preferring non-Gaussian noise instead of conventional pseudo-noise (PN) sequence is to overcome the drawback of self-repeating noise-like sequences which are detectable due to the periodic behavior of the autocorrelation function of PN sequences. Having infinite second order moment in α-stable random carrier offers secrecy of the information due to the non-constant autocorrelation behavior. The bit error rate (BER) performance of the proposed method is illustrated by Monte Carlo simulations with respect to various characteristic exponent values and different data length.

Non-Gaussian Density Processes Arising from Non-Poisson Systems of Independent Brownian Motions

1998 ◽  
Vol 35 (01) ◽  
pp. 213-220
Author(s):  
Raisa E. Feldman ◽  
Srikanth K. Iyer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stochastic Partial Differential Equation ◽  
Particle System ◽  
Initial Distribution ◽  
Martingale Measure ◽  
Partial Differential ◽  
Gaussian Density ◽  
Non Gaussian ◽  
Density Process

The Brownian density process is a Gaussian distribution-valued process. It can be defined either as a limit of a functional over a Poisson system of independent Brownian particles or as a solution of a stochastic partial differential equation with respect to Gaussian martingale measure. We show that, with an appropriate change in the initial distribution of the infinite particle system, the limiting density process is non-Gaussian and it solves a stochastic partial differential equation where the initial measure and the driving measure are non-Gaussian, possibly having infinite second moment.

scholarly journals When Can Non-Gaussian Density Fields Produce a Gaussian Sachs-Wolfe Effect?

1995 ◽  
Vol 446 ◽  
pp. 44 ◽  
Author(s):  
Robert J. Scherrer ◽  
Robert K. Schaefer
Keyword(s):  
Gaussian Density ◽  
Non Gaussian
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