2,405 research outputs found
On the streaming model for redshift-space distortions
The streaming model describes the mapping between real and redshift space for
2-point clustering statistics. Its key element is the probability density
function (PDF) of line-of-sight pairwise peculiar velocities. Following a
kinetic-theory approach, we derive the fundamental equations of the streaming
model for ordered and unordered pairs. In the first case, we recover the
classic equation while we demonstrate that modifications are necessary for
unordered pairs. We then discuss several statistical properties of the pairwise
velocities for DM particles and haloes by using a suite of high-resolution
-body simulations. We test the often used Gaussian ansatz for the PDF of
pairwise velocities and discuss its limitations. Finally, we introduce a
mixture of Gaussians which is known in statistics as the generalised hyperbolic
distribution and show that it provides an accurate fit to the PDF. Once
inserted in the streaming equation, the fit yields an excellent description of
redshift-space correlations at all scales that vastly outperforms the Gaussian
and exponential approximations. Using a principal-component analysis, we reduce
the complexity of our model for large redshift-space separations. Our results
increase the robustness of studies of anisotropic galaxy clustering and are
useful for extending them towards smaller scales in order to test theories of
gravity and interacting dark-energy models.Comment: 22 pages, 20 figures, accepted for publication in MNRA
On the use of the l(2)-norm for texture analysis of polarimetric SAR data
In this paper, the use of the l2-norm, or Span, of the scattering vectors is suggested for texture analysis of polarimetric synthetic aperture radar (SAR) data, with the benefits that we need neither an analysis of the polarimetric channels separately nor a filtering of the data to analyze the statistics. Based on the product model, the distribution of the l2-norm is studied. Closed expressions of the probability density functions under the assumptions of several texture distributions are provided. To utilize the statistical properties of the l2-norm, quantities including normalized moments and log-cumulants are derived, along with corresponding estimators and estimation variances. Results on both simulated and real SAR data show that the use of statistics based on the l2-norm brings advantages in several aspects with respect to the normalized intensity moments and matrix variate log-cumulants.Peer ReviewedPostprint (published version
Statistical applications of the multivariate skew-normal distribution
Azzalini & Dalla Valle (1996) have recently discussed the multivariate
skew-normal distribution which extends the class of normal distributions by the
addition of a shape parameter. The first part of the present paper examines
further probabilistic properties of the distribution, with special emphasis on
aspects of statistical relevance. Inferential and other statistical issues are
discussed in the following part, with applications to some multivariate
statistics problems, illustrated by numerical examples. Finally, a further
extension is described which introduces a skewing factor of an elliptical
density.Comment: full-length version of the published paper, 32 pages, with 7 figures,
uses psfra
Condensation and Metastability in the 2D Potts Model
For the first order transition of the Ising model below , Isakov has
proven that the free energy possesses an essential singularity in the applied
field. Such a singularity in the control parameter, anticipated by condensation
theory, is believed to be a generic feature of first order transitions, but too
weak to be observable. We study these issues for the temperature driven
transition of the states 2D Potts model at . Adapting the droplet
model to this case, we relate its parameters to the critical properties at
and confront the free energy to the many informations brought by previous
works. The essential singularity predicted at the transition temperature leads
to observable effects in numerical data. On a finite lattice, a metastability
domain of temperatures is identified, which shrinks to zero in the
thermodynamical limit. ~Comment: 32 pages, 6 figures, Late
Low-temperature properties of some disordered systems from the statistical properties of nearly degenerate two-level excitations
The thermal fluctuations that exist at very low temperature in disordered
systems are often attributed to the existence of some two-level excitations. In
this paper, we revisit this question via the explicit studies of the following
1D models (i) a particle in 1D random potentials (ii) the random field Ising
chain with continuous disorder distribution. In both cases, we define precisely
the `two-level' excitations and their statistical properties, and we show that
their contributions to various observables are in full agreement at low
temperature with the the rigorous results obtained independently. The
statistical properties of these two-level excitations moreover yield simple
identities at order in temperature for some generating functions of thermal
cumulants. For the random-field Ising chain, in the regime where the Imry-Ma
length is large, we obtain that the specific heat is dominated by small
non-universal excitations, that depend on the details of the disorder
distribution, whereas the magnetic susceptibility and the Edwards-Anderson
order parameter are dominated by universal large excitations, whose statistical
properties only depend on the variance of the initial disorder via the Imry-Ma
length.Comment: 19 pages, 4 figure
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