17,668 research outputs found
On the Anti-Wishart distribution
We provide the probability distribution function of matrix elements each of
which is the inner product of two vectors.
The vectors we are considering here are independently distributed but not
necessarily Gaussian variables.
When the number of components M of each vector is greater than the number of
vectors N, one has a symmetric matrix.
When and the components of each vector are independent Gaussian
variables, the distribution function of the matrix elements was
obtained by Wishart in 1928.
When N > M, what we called the ``Anti-Wishart'' case, the matrix elements are
no longer completely independent because the true degrees of freedom becomes
smaller than the number of matrix elements. Due to this singular nature,
analytical derivation of the probability distribution function is much more
involved than the corresponding Wishart case. For a class of general random
vectors, we obtain the analytical distribution function in a closed form, which
is a product of various factors and delta function constraints, composed of
various determinants. The distribution function of the matrix element for the
case with the same class of random vectors is also obtained as a
by-product. Our result is closely related to and should be valuable for the
study of random magnet problem and information redundancy problem.Comment: to appear in Physica
Does a change in debt structure matter in earnings management? the application of nonlinear panel threshold test
In this study, we apply HansenĂÂĄĂŠs (1999) nonlinear panel threshold test, the most powerful test of its kind, to investigate the relationship between debt ratio and earnings management of 474 selected Taiwan-listed companies during the September 2002 - June 2005 period. Rather than a fixed positive relation that is determined from the OLS, our empirical results strongly suggest that when a firmĂÂĄĂŠs debt ratio exceeds 46.79% and 62.17%, its debt structure changes, which in turn leads to changes in earnings management. With an increase in debt ratio, managers tend to manage earnings to a greater extent and at a higher speed. In other words, the threshold effect of debt on the relationship between debt ratio and earnings management generates an increasingly positive impact. These empirical results provide concerned investors and authorities with an enhanced understanding of earnings management, as manipulated by managers confronted with different debt structures.
Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model
We study the long-distance asymptotic behavior of various correlation
functions for the one-dimensional (1D) attractive Hubbard model in a partially
polarized phase through the Bethe ansatz and conformal field theory approaches.
We particularly find the oscillating behavior of these correlation functions
with spatial power-law decay, of which the pair (spin) correlation function
oscillates with a frequency (). Here is the mismatch in the Fermi surfaces of
spin-up and spin-down particles. Consequently, the pair correlation function in
momentum space has peaks at the mismatch , which has been
observed in recent numerical work on this model. These singular peaks in
momentum space together with the spatial oscillation suggest an analog of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The
parameter representing the lattice effect becomes prominent in critical
exponents which determine the power-law decay of all correlation functions. We
point out that the backscattering of unpaired fermions and bound pairs within
their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.Comment: 26 pages, 4 figures, published version, a series of study on the 1D
attractive Hubbard model, few typos were corrected, references were added,
also see arXiv:1708.07784 and arXiv:1708.0777
FFLO correlation and free fluids in the one-dimensional attractive Hubbard model
In this Rapid Communication we show that low energy macroscopic properties of
the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound
pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations
of the model, we first determine the low temperature phase diagram and
analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing
correlation function for the partially-polarized phase. We then show that for
such a FFLO-like state in the low density regime the effective chemical
potentials of bound pairs and unpaired fermions behave like two free fluids.
Consequently, the susceptibility, compressibility and specific heat obey simple
additivity rules, indicating the `free' particle nature of interacting fermions
on a 1D lattice. In contrast to the continuum Fermi gases, the correlation
critical exponents and thermodynamics of the attractive Hubbard model
essentially depend on two lattice interacting parameters. Finally, we study
scaling functions, the Wilson ratio and susceptibility which provide universal
macroscopic properties/dimensionless constants of interacting fermions at low
energy.Comment: In this Letter we analytically study FFLO pairing correlation and the
universal nature of the FFLO-like state. More detailed studies of this model
will be presented in arXiv:1710.08742 and arXiv:1708.0778
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