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

Simple Scheme for Efficient Linear Optics Quantum Gates

We describe the construction of a conditional quantum control-not (CNOT) gate from linear optical elements following the program of Knill, Laflamme and Milburn [Nature {\bf 409}, 46 (2001)]. We show that the basic operation of this gate can be tested using current technology. We then simplify the scheme significantly.Comment: Problems with PDF figures correcte

Magnification relations of quad lenses and applications on Einstein crosses

In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It can also explain that for many observed fold image pairs, the fluxes of the Fermat minimum images are apt to be larger than those of the saddle images. We define a new quantity cross relation which describes the magnification discrepancy between two minimum images and two saddle images. Distance ratio is also defined as the ratio of the distance of two saddle images to that of two minimum images. We calculate the cross relations and distance ratios for nine observed Einstein crosses. In theory, for most of the quad lens models, the cross relations decrease as the distance ratios increase. In observation, the cross relations of the nine samples do not agree with the quad lens models very well, nevertheless, the cross relations of the nine samples do not give obvious evidence for anomalous flux ratio as the cusp and fold types do. Then, we discuss several reasons for the disagreement, and expect good consistencies for more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA

Central limit theorem for Hotelling's T2T^2 statistic under large dimension

In this paper we prove the central limit theorem for Hotelling's $T^2$ statistic when the dimension of the random vectors is proportional to the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-AAP742 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Time-Varying Priority Queuing Models for Human Dynamics

Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of interest, the priority of which may vary with time due to the agent's "state of mind." However, its execution is disrupted by other tasks of random priorities. By considering the priority of the task of interest either decreasing or increasing algebraically in time, we analytically obtain and numerically confirm the bimodal and unimodal waiting time distributions with power-law decaying tails, respectively. These results are also compared to the updating time distribution of papers in the arXiv.org and the processing time distribution of papers in Physical Review journals. Our analysis helps to understand human task execution in a more realistic scenario.Comment: 8 pages, 6 figure

High-energy kink in high-temperature superconductors

In conventional metals, electron-phonon coupling, or the phonon-mediated interaction between electrons, has long been known to be the pairing interaction responsible for the superconductivity. The strength of this interaction essentially determines the superconducting transition temperature TC. One manifestation of electron-phonon coupling is a mass renormalization of the electronic dispersion at the energy scale associated with the phonons. This renormalization is directly observable in photoemission experiments. In contrast, there remains little consensus on the pairing mechanism in cuprate high temperature superconductors. The recent observation of similar renormalization effects in cuprates has raised the hope that the mechanism of high temperature superconductivity may finally be resolved. The focus has been on the low energy renormalization and associated "kink" in the dispersion at around 50 meV. However at that energy scale, there are multiple candidates including phonon branches, structure in the spin-fluctuation spectrum, and the superconducting gap itself, making the unique identification of the excitation responsible for the kink difficult. Here we show that the low-energy renormalization at ~50 meV is only a small component of the total renormalization, the majority of which occurs at an order of magnitude higher energy (~350 meV). This high energy kink poses a new challenge for the physics of the cuprates. Its role in superconductivity and relation to the low-energy kink remains to be determined.Comment: 13 pages, 4 figure

Tunneling into Multiwalled Carbon Nanotubes: Coulomb Blockade and Fano Resonance

Tunneling spectroscopy measurements of single tunnel junctions formed between multiwalled carbon nanotubes (MWNTs) and a normal metal are reported. Intrinsic Coulomb interactions in the MWNTs give rise to a strong zero-bias suppression of a tunneling density of states (TDOS) that can be fitted numerically to the environmental quantum-fluctuation (EQF) theory. An asymmetric conductance anomaly near zero bias is found at low temperatures and interpreted as Fano resonance in the strong tunneling regime.Comment: 4 pages, 4 figure