3,444 research outputs found
Spectral density asymptotics for Gaussian and Laguerre -ensembles in the exponentially small region
The first two terms in the large asymptotic expansion of the
moment of the characteristic polynomial for the Gaussian and Laguerre
-ensembles are calculated. This is used to compute the asymptotic
expansion of the spectral density in these ensembles, in the exponentially
small region outside the leading support, up to terms . The leading form
of the right tail of the distribution of the largest eigenvalue is given by the
density in this regime. It is demonstrated that there is a scaling from this,
to the right tail asymptotics for the distribution of the largest eigenvalue at
the soft edge.Comment: 19 page
Quantum conductance problems and the Jacobi ensemble
In one dimensional transport problems the scattering matrix is decomposed
into a block structure corresponding to reflection and transmission matrices at
the two ends. For a random unitary matrix, the singular value probability
distribution function of these blocks is calculated. The same is done when
is constrained to be symmetric, or to be self dual quaternion real, or when
has real elements, or has real quaternion elements. Three methods are used:
metric forms; a variant of the Ingham-Seigel matrix integral; and a theorem
specifying the Jacobi random matrix ensemble in terms of Wishart distributed
matrices.Comment: 10 page
Applications and generalizations of Fisher-Hartwig asymptotics
Fisher-Hartwig asymptotics refers to the large form of a class of
Toeplitz determinants with singular generating functions. This class of
Toeplitz determinants occurs in the study of the spin-spin correlations for the
two-dimensional Ising model, and the ground state density matrix of the
impenetrable Bose gas, amongst other problems in mathematical physics. We give
a new application of the original Fisher-Hartwig formula to the asymptotic
decay of the Ising correlations above , while the study of the Bose gas
density matrix leads us to generalize the Fisher-Hartwig formula to the
asymptotic form of random matrix averages over the classical groups and the
Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our
generalizations is that they extend to Hankel determinants the Fisher-Hartwig
asymptotic form known for Toeplitz determinants.Comment: 25 page
Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
The two-dimensional one-component plasma (2dOCP) is a system of mobile
particles of the same charge on a surface with a neutralising background.
The Boltzmann factor of the 2dOCP at temperature can be expressed as a
Vandermonde determinant to the power . Recent advances in
the theory of symmetric and anti-symmetric Jack polymonials provide an
efficient way to expand this power of the Vandermonde in their monomial basis,
allowing the computation of several thermodynamic and structural properties of
the 2dOCP for values up to 14 and equal to 4, 6 and 8. In this
work, we explore two applications of this formalism to study the moments of the
pair correlation function of the 2dOCP on a sphere, and the distribution of
radial linear statistics of the 2dOCP in the plane
1-[2-(Carboxymethoxy)phenyl]-N-(4-chlorophenyl)methanimine oxide
Peer reviewedPublisher PD
Eigenvalue distributions for some correlated complex sample covariance matrices
The distributions of the smallest and largest eigenvalues for the matrix
product , where is an complex Gaussian matrix
with correlations both along rows and down columns, are expressed as determinants. In the case of correlation along rows, these expressions are
computationally more efficient than those involving sums over partitions and
Schur polynomials reported recently for the same distributions.Comment: 11 page
Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues
We study the transition in conductance properties of chaotic mesoscopic
cavities as time-reversal symmetry is broken. We consider the Brownian motion
model for transmission eigenvalues for both types of transitions, viz.,
orthogonal-unitary and symplectic-unitary crossovers depending on the presence
or absence of spin-rotation symmetry of the electron. In both cases the
crossover is governed by a Brownian motion parameter {\tau}, which measures the
extent of time-reversal symmetry breaking. It is shown that the results
obtained correspond to the Jacobi crossover ensembles of random matrices. We
derive the level density and the correlation functions of higher orders for the
transmission eigenvalues. We also obtain the exact expressions for the average
conductance, average shot-noise power and variance of conductance, as functions
of {\tau}, for arbitrary number of modes (channels) in the two leads connected
to the cavity. Moreover, we give the asymptotic result for the variance of
shot-noise power for both the crossovers, the exact results being too long. In
the {\tau} \rightarrow 0 and {\tau} \rightarrow \infty limits the known results
for the orthogonal (or symplectic) and unitary ensembles are reproduced. In the
weak time-reversal symmetry breaking regime our results are shown to be in
agreement with the semiclassical predictions.Comment: 24 pages, 5 figure
Screening and diagnostic assessment of neurodevelopmental disorders in a male prison
Purpose
The purpose of this paper is to identify neurodevelopmental disorders and difficulties (NDD) in a male prison. The study used standardised tools to carry out screening and diagnostic assessment of the attention deficit hyperactivity disorder (ADHD), autism spectrum disorder (ASD) and intellectual disability (ID).
Design/methodology/approach
The ADHD self-report scale, 20-item autism quotient and the Learning Disability Screening Questionnaire were used to screen 240 male prisoners. Prisoners who screened positive on one or more of these scales or self-reported a diagnosis of ADHD, ASD or ID were further assessed using the diagnostic interview for ADHD in adults, adapted Autism Diagnostic Observation Schedule and the Quick Test.
Findings
Of the 87 prisoners who screened positive for NDD and were further assessed, 70 met the study’s diagnostic criteria for ADHD, ASD or ID. Most of those with NDD (51 per cent) had previously gone unrecognised and a high proportion (51 per cent) were identified through staff- or self-referral to the study.
Originality/value
The study demonstrated that improving awareness and providing access to skilled, standardised assessment within a male prison can result in increased recognition and identification of NDD
Asymptotic corrections to the eigenvalue density of the GUE and LUE
We obtain correction terms to the large N asymptotic expansions of the
eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of
random N by N matrices, both in the bulk of the spectrum and near the spectral
edge. This is achieved by using the well known orthogonal polynomial expression
for the kernel to construct a double contour integral representation for the
density, to which we apply the saddle point method. The main correction to the
bulk density is oscillatory in N and depends on the distribution function of
the limiting density, while the corrections to the Airy kernel at the soft edge
are again expressed in terms of the Airy function and its first derivative. We
demonstrate numerically that these expansions are very accurate. A matching is
exhibited between the asymptotic expansion of the bulk density, expanded about
the edge, and the asymptotic expansion of the edge density, expanded into the
bulk.Comment: 14 pages, 4 figure
Recommended from our members
Income Trends among U.S. Residential Rooftop Solar Adopters
Berkeley Lab tracks and analyzes solar-adopter demographic characteristics. A central element of this work is an annual report describing income trends of residential solar adopters over time and across geographies. The report is based on household-level income estimates for single-family residential solar adopters across the United States, and is intended to serve as a foundational reference document for policy-makers, industry stakeholders, and other researchers interested in demographic trends among residential solar adopters. The report is published with an accompanying interactive data visualization tool that allows users to further explore the underlying data.
In addition to the annual report, Berkeley Lab also conducts targeted topical analyses on issues related to solar-adopter demographics and provides direct analytical support to organizations working to expand access to solar energy among low-to-moderate income households. Requests for analytical support may be submitted through this form: "https://docs.google.com/forms/d/e/1FAIpQLSfOauinm2NRF-9J39aDh3447F9FDTOsP3tpMHJLzH_orKoTpw/viewform" target="_blank">online form. 
- …