128 research outputs found
On Orthogonal and Symplectic Matrix Ensembles
The focus of this paper is on the probability, , that a set
consisting of a finite union of intervals contains no eigenvalues for the
finite Gaussian Orthogonal () and Gaussian Symplectic ()
Ensembles and their respective scaling limits both in the bulk and at the edge
of the spectrum. We show how these probabilities can be expressed in terms of
quantities arising in the corresponding unitary () ensembles. Our most
explicit new results concern the distribution of the largest eigenvalue in each
of these ensembles. In the edge scaling limit we show that these largest
eigenvalue distributions are given in terms of a particular Painlev\'e II
function.Comment: 34 pages. LaTeX file with one figure. To appear in Commun. Math.
Physic
An anisotropic cosmological model with isotropic background radiation
We present an exact solution of Einstein equations that describes a Bianchi
type III spacetime with conformal expansion. The matter content is given by an
anisotropic scalar field and two perfect fluids representing dust and isotropic
radiation. Based on this solution, we construct a cosmological model that
respects the evolution of the scale factor predicted in standard cosmology.Comment: 4 pages; contribution to the Proceedings of the 24th Spanish
Relativity Meeting (ERE2001
How close can an Inhomogeneous Universe mimic the Concordance Model?
Recently, spatially inhomogeneous cosmological models have been proposed as
an alternative to the LCDM model, with the aim of reproducing the late time
dynamics of the Universe without introducing a cosmological constant or dark
energy. This paper investigates the possibility of distinguishing such models
from the standard LCDM using background or large scale structure data. It also
illustrates and emphasizes the necessity of testing the Copernican principle in
order to confront the tests of general relativity with the large scale
structure.Comment: 15 pages, 7 figure
Fredholm Determinants, Differential Equations and Matrix Models
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to
Fredholm determinants of integral operators with kernel of the form (phi(x)
psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm
determinants of integral operators having kernel of this form and where the
underlying set is a union of open intervals. The emphasis is on the
determinants thought of as functions of the end-points of these intervals. We
show that these Fredholm determinants with kernels of the general form
described above are expressible in terms of solutions of systems of PDE's as
long as phi and psi satisfy a certain type of differentiation formula. There is
also an exponential variant of this analysis which includes the circular
ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only
the abstract and decreases length of typeset versio
Qualitative Properties of Magnetic Fields in Scalar Field Cosmology
We study the qualitative properties of the class of spatially homogeneous
Bianchi VI_o cosmological models containing a perfect fluid with a linear
equation of state, a scalar field with an exponential potential and a uniform
cosmic magnetic field, using dynamical systems techniques. We find that all
models evolve away from an expanding massless scalar field model in which the
matter and the magnetic field are negligible dynamically. We also find that for
a particular range of parameter values the models evolve towards the usual
power-law inflationary model (with no magnetic field) and, furthermore, we
conclude that inflation is not fundamentally affected by the presence of a
uniform primordial magnetic field. We investigate the physical properties of
the Bianchi I magnetic field models in some detail.Comment: 12 pages, 2 figures in REVTeX format. to appear in Phys. Rev.
Fredholm determinants and pole-free solutions to the noncommutative Painleve' II equation
We extend the formalism of integrable operators a' la
Its-Izergin-Korepin-Slavnov to matrix-valued convolution operators on a
semi-infinite interval and to matrix integral operators with a kernel of the
form E_1^T(x) E_2(y)/(x+y) thus proving that their resolvent operators can be
expressed in terms of solutions of some specific Riemann-Hilbert problems. We
also describe some applications, mainly to a noncommutative version of
Painleve' II (recently introduced by Retakh and Rubtsov), a related
noncommutative equation of Painleve' type. We construct a particular family of
solutions of the noncommutative Painleve' II that are pole-free (for real
values of the variables) and hence analogous to the Hastings-McLeod solution of
(commutative) Painleve' II. Such a solution plays the same role as its
commutative counterpart relative to the Tracy-Widom theorem, but for the
computation of the Fredholm determinant of a matrix version of the Airy kernel.Comment: 46 pages, no figures (oddly
The Five Factor Model of personality and evaluation of drug consumption risk
The problem of evaluating an individual's risk of drug consumption and misuse
is highly important. An online survey methodology was employed to collect data
including Big Five personality traits (NEO-FFI-R), impulsivity (BIS-11),
sensation seeking (ImpSS), and demographic information. The data set contained
information on the consumption of 18 central nervous system psychoactive drugs.
Correlation analysis demonstrated the existence of groups of drugs with
strongly correlated consumption patterns. Three correlation pleiades were
identified, named by the central drug in the pleiade: ecstasy, heroin, and
benzodiazepines pleiades. An exhaustive search was performed to select the most
effective subset of input features and data mining methods to classify users
and non-users for each drug and pleiad. A number of classification methods were
employed (decision tree, random forest, -nearest neighbors, linear
discriminant analysis, Gaussian mixture, probability density function
estimation, logistic regression and na{\"i}ve Bayes) and the most effective
classifier was selected for each drug. The quality of classification was
surprisingly high with sensitivity and specificity (evaluated by leave-one-out
cross-validation) being greater than 70\% for almost all classification tasks.
The best results with sensitivity and specificity being greater than 75\% were
achieved for cannabis, crack, ecstasy, legal highs, LSD, and volatile substance
abuse (VSA).Comment: Significantly extended report with 67 pages, 27 tables, 21 figure
CMB observations in LTB universes: Part I: Matching peak positions in the CMB spectrum
Acoustic peaks in the spectrum of the cosmic microwave background in
spherically symmetric inhomogeneous cosmological models are studied. At the
photon-baryon decoupling epoch, the universe may be assumed to be dominated by
non-relativistic matter, and thus we may treat radiation as a test field in the
universe filled with dust which is described by the Lema\^itre-Tolman-Bondi
(LTB) solution. First, we give an LTB model whose distance-redshift relation
agrees with that of the concordance CDM model in the whole redshift
domain and which is well approximated by the Einstein-de Sitter universe at and
before decoupling. We determine the decoupling epoch in this LTB universe by
Gamow's criterion and then calculate the positions of acoustic peaks. Thus
obtained results are not consistent with the WMAP data. However, we find that
one can fit the peak positions by appropriately modifying the LTB model,
namely, by allowing the deviation of the distance-redshift relation from that
of the concordance CDM model at where no observational data are
available at present. Thus there is still a possibility of explaining the
apparent accelerated expansion of the universe by inhomogeneity without
resorting to dark energy if we abandon the Copernican principle. Even if we do
not take this extreme attitude, it also suggests that local, isotropic
inhomogeneities around us may seriously affect the determination of the density
contents of the universe unless the possible existence of such inhomogeneities
is properly taken into account.Comment: 20 pages, 5 figure
Light propagation in statistically homogeneous and isotropic universes with general matter content
We derive the relationship of the redshift and the angular diameter distance
to the average expansion rate for universes which are statistically homogeneous
and isotropic and where the distribution evolves slowly, but which have
otherwise arbitrary geometry and matter content. The relevant average expansion
rate is selected by the observable redshift and the assumed symmetry properties
of the spacetime. We show why light deflection and shear remain small. We write
down the evolution equations for the average expansion rate and discuss the
validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular
diameter distance and two typos. No change in result
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