We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that the maximum likelihood estimator is strongly consistent, if the scale parameters of the component uniform distributions are restricted from below by exp(−nd), 0 < d < 1, where n is the sample size.

The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a test we apply the method to interacting spinless fermions with modulated hopping. We calculate the finite-size corrections to the energy gap and the Drude we...

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG) applied to 2D classical systems. Numerical efficiency of this approximation is inve...

An Ornstein-Zernike approximation for the two-body correlation function embodying thermodynamic consistency is applied to a system of classical Heisenberg spins on a three-dimensional lattice. The consistency condition determined in a previous work is supplemented by introducing a simplified expression for the meansquare fluctuations of the spin on each lattice site. The thermodynamics and the ...

We generalize the self-consistent Ornstein-Zernike approximation (SCOZA) to a fluid of particles with a pair potential consisting of a hard-core repulsion and a linear combination of Sogami-Ise tails, w(r)=-epsilonsigma summation operator (nu)(K(nu)/r+L(nu)z(nu))e(-z(nu)(r-sigma)). The formulation and implementation of the SCOZA takes advantage of the availability of semianalytic results for su...

The self-consistent Ornstein-Zernike approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon te...