206,950 research outputs found
On the Spectral Properties of Symmetric Functions
We characterize the approximate monomial complexity, sign monomial complexity , and the approximate L 1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L 1 norm solves the main conjecture in [AFH12]. As an application of the characterization of the sign monomial complexity, we prove a conjecture in [ZS09] and provide a characterization for the unbounded-error communication complexity of symmetric-xor functions
Multivariate Krawtchouk polynomials and composition birth and death processes
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the
multinomial distribution, and summarizes their properties as a review. The
multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets
of functions defined on each of N multinomial trials. The dual multivariate
Krawtchouk polynomials, which also have a polynomial structure, are seen to
occur naturally as spectral orthogonal polynomials in a Karlin and McGregor
spectral representation of transition functions in a composition birth and
death process. In this Markov composition process in continuous time there are
N independent and identically distributed birth and death processes each with
support 0,1, .... The state space in the composition process is the number of
processes in the different states 0,1,... Dealing with the spectral
representation requires new extensions of the multivariate Krawtchouk
polynomials to orthogonal polynomials on a multinomial distribution with a
countable infinity of states
In medium T-matrix for nuclear matter with three-body forces - binding energy and single particle properties
We present spectral calculations of nuclear matter properties including
three-body forces. Within the in-medium T-matrix approach, implemented with the
CD-Bonn and Nijmegen potentials plus the three-nucleon Urbana interaction, we
compute the energy per particle in symmetric and neutron matter. The three-body
forces are included via an effective density dependent two-body force in the
in-medium T-matrix equations. After fine tuning the parameters of the
three-body force to reproduce the phenomenological saturation point in
symmetric nuclear matter, we calculate the incompressibility and the energy per
particle in neutron matter. We find a soft equation of state in symmetric
nuclear matter but a relatively large value of the symmetry energy. We study
the the influence of the three-body forces on the single-particle properties.
For symmetric matter the spectral function is broadened at all momenta and all
densities, while an opposite effect is found for the case of neutrons only.
Noticeable modification of the spectral functions are realized only for
densities above the saturation density. The modifications of the self-energy
and the effective mass are not very large and appear to be strongly suppressed
above the Fermi momentum.Comment: 20 pages, 11 figure
Essential spectrum and Weyl asymptotics for discrete Laplacians
In this paper, we investigate spectral properties of discrete Laplacians. Our
study is based on the Hardy inequality and the use of super-harmonic functions.
We recover and improve lower bounds for the bottom of the spectrum and of the
essential spectrum. In some situation, we obtain Weyl asymptotics for the
eigenvalues. We also provide a probabilistic representation of super-harmonic
functions. Using coupling arguments, we set comparison results for the bottom
of the spectrum, the bottom of the essential spectrum and the stochastic
completeness of different discrete Laplacians. The class of weakly spherically
symmetric graphs is also studied in full detail
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