Central limit theorem for signal-to-interference ratio of reduced rank linear receiver

Let $\mathbf{s}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk})^T,$ with $\{v_{ik},i,k=1,...\}$ independent and identically distributed complex random variables. Write $\mathbf{S}_k=(\mathbf{s}_1,...,\mathbf {s}_{k-1},\mathbf{s}_{k+1},... ,\mathbf{s}_K),$ $\mathbf{P}_k=\operatorname {diag}(p_1,...,p_{k-1},p_{k+1},...,p_K)$, $\mathbf{R}_k=(\mathbf{S}_k\mathbf{P}_k\mathbf{S}_k^*+\sigma ^2\mathbf{I})$ and $\mathbf{A}_{km}=[\mathbf{s}_k,\mathbf{R}_k\mathbf{s}_k,... ,\mathbf{R}_k^{m-1}\mathbf{s}_k]$. Define $\beta_{km}=p_k\mathbf{s}_k^*\mathbf{A}_{km}(\mathbf {A}_{km}^*\times\ mathbf{R}_k\mathbf{A}_{km})^{-1}\mathbf{A}_{km}^*\mathbf{s}_k$, referred to as the signal-to-interference ratio (SIR) of user$k$under the multistage Wiener (MSW) receiver in a wireless communication system. It is proved that the output SIR under the MSW and the mutual information statistic under the matched filter (MF) are both asymptotic Gaussian when$N/K\to c>0$. Moreover, we provide a central limit theorem for linear spectral statistics of eigenvalues and eigenvectors of sample covariance matrices, which is a supplement of Theorem 2 in Bai, Miao and Pan [Ann. Probab. 35 (2007) 1532--1572]. And we also improve Theorem 1.1 in Bai and Silverstein [Ann. Probab. 32 (2004) 553--605].Comment: Published in at http://dx.doi.org/10.1214/07-AAP477 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adsorption of Externally Stretched Two-Dimensional Flexible and Semi-flexible Polymers near an Attractive Wall

We study analytically a model of a two dimensional, partially directed, flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction smaller than the non-sequential nearest neighbor attraction, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for greater than, the fraction of monomers at the wall undergoes a first order transition from unity at low temperature and small force, to zero at higher temperatures and forces. We present phase diagram for this transition. Our results are confirmed by Monte-Carlo simulations.Comment: 15 pages, 6 figure

Neutron halo in deformed nuclei from a relativistic Hartree-Bogoliubov model in a Woods-Saxon basis

Halo phenomenon in deformed nuclei is studied by using a fully self-consistent deformed relativistic Hartree-Bogoliubov model in a spherical Woods-Saxon basis with the proper asymptotic behavior at large distance from the nuclear center. Taking a deformed neutron-rich and weakly bound nucleus $^{44}$Mg as an example and by examining contributions of the halo, deformation effects, and large spatial extensions, we show a decoupling of the halo orbitals from the deformation of the core.Comment: 6 pages, 2 figures, to appear in the proceedings of the International Nuclear Physics Conference (INPC 2010), July 4-9 2010, Vancouve

Conditions for Nondistortion Interrogation of Quantum System

Under some physical considerations, we present a universal formulation to study the possibility of localizing a quantum object in a given region without disturbing its unknown internal state. When the interaction between the object and probe wave function takes place only once, we prove the necessary and sufficient condition that the object's presence can be detected in an initial state preserving way. Meanwhile, a conditioned optimal interrogation probability is obtained.Comment: 5 pages, Revtex, 1 figures, Presentation improved, corollary 1 added. To appear in Europhysics Letter

A complement to Le Cam's theorem

This paper examines asymptotic equivalence in the sense of Le Cam between density estimation experiments and the accompanying Poisson experiments. The significance of asymptotic equivalence is that all asymptotically optimal statistical procedures can be carried over from one experiment to the other. The equivalence given here is established under a weak assumption on the parameter space $\mathcal{F}$. In particular, a sharp Besov smoothness condition is given on $\mathcal{F}$ which is sufficient for Poissonization, namely, if $\mathcal{F}$ is in a Besov ball $B_{p,q}^{\alpha}(M)$ with $\alpha p>1/2$. Examples show Poissonization is not possible whenever $\alpha p<1/2$. In addition, asymptotic equivalence of the density estimation model and the accompanying Poisson experiment is established for all compact subsets of $C([0,1]^m)$, a condition which includes all H\"{o}lder balls with smoothness $\alpha>0$.Comment: Published at http://dx.doi.org/10.1214/009053607000000091 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Density-dependent deformed relativistic Hartree-Bogoliubov theory in continuum

The deformed relativistic Hartree-Bogoliubov theory in continuum with the density-dependent meson-nucleon couplings is developed. The formulism is briefly presented with the emphasis on handling the density-dependent couplings, meson fields, and potentials in axially deformed system with partial wave method. Taking the neutron-rich nucleus $^{38}$Mg as an example, the newly developed code is verified by the spherical relativistic continuum Hartree-Bogoliubov calculations, where only the spherical components of the densities are considered. When the deformation is included self-consistently, it is shown that the spherical components of density-dependent coupling strengths are dominant, while the contributions from low-order deformed components are not negligible.Comment: 5 pages, 3 figures, and 1 tabl

Sensitivity of neutron to proton ratio toward the high density behavior of symmetry energy in heavy-ion collisions

The symmetry energy at sub and supra-saturation densities has a great importance in understanding the exact nature of asymmetric nuclear matter as well as neutron star, but, it is poor known, especially at supra-saturation densities. We will demonstrate here that the neutron to proton ratios from different kind of fragments is able to determine the supra-saturation behavior of symmetry energy or not. For this purpose, a series of Sn isotopes are simulated at different incident energies using the Isospin Quantum Molecular Dynamics (IQMD) model with either a soft or a stiff symmetry energy for the present study. It is found that the single neutron to proton ratio from free nucleons as well as LCP's is sensitive towards the symmetry energy, incident energy as well as isospin asymmetry of the system. However, with the double neutron to proton ratio, it is true only for the free nucleons. It is possible to study the high density behavior of symmetry energy by using the neutron to proton ratio from free nucleons.Comment: 11 Pages, 9 Figure