43,448 research outputs found

### 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

### Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero

Let $\mathbf{X}_p=(\mathbf{s}_1,...,\mathbf{s}_n)=(X_{ij})_{p \times n}$
where $X_{ij}$'s are independent and identically distributed (i.i.d.) random
variables with $EX_{11}=0,EX_{11}^2=1$ and $EX_{11}^4<\infty$. It is showed
that the largest eigenvalue of the random matrix
$\mathbf{A}_p=\frac{1}{2\sqrt{np}}(\mathbf{X}_p\mathbf{X}_p^{\prime}-n\mathbf{I}_p)$
tends to 1 almost surely as $p\rightarrow\infty,n\rightarrow\infty$ with
$p/n\rightarrow0$.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ381 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

### Independence Test for High Dimensional Random Vectors

This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The asymptotic distributions of the test statistic under the null and local alternative hypotheses are established as dimensionality and the sample size of the data are comparable. We apply this test to examine multiple MA(1) and AR(1) models, panel data models with some spatial cross-sectional structures. In addition, in a flexible applied fashion, the proposed test can capture some dependent but uncorrelated structures, for example, nonlinear MA(1) models, multiple ARCH(1) models and vandermonde matrices. Simulation results are provided for detecting these dependent structures. An empirical study of dependence between closed stock prices of several companies from New York Stock Exchange (NYSE) demonstrates that the feature of cross-sectional dependence is popular in stock marketsIndependence test, cross-sectional dependence, empirical spectral distribution, characteristic function, Marcenko-Pastur Law

### Quasi-exactly solvable cases of the N-dimensional symmetric quartic anharmonic oscillator

The O(N) invariant quartic anharmonic oscillator is shown to be exactly
solvable if the interaction parameter satisfies special conditions. The problem
is directly related to that of a quantum double well anharmonic oscillator in
an external field. A finite dimensional matrix equation for the problem is
constructed explicitly, along with analytical expressions for some excited
states in the system. The corresponding Niven equations for determining the
polynomial solutions for the problem are given.Comment: 7 pages, RevTeX4. A discussion on the N=1 case has been added with
the boundary condition properly treate

### 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

### New Anisotropic Behavior of Quantum Hall Resistance in (110) GaAs Heterostructures at mK Temperatures and Fractional Filling Factors

Transport experiments in high mobility (110) GaAs heterostructures have been
performed at very low temperatures 8 mK. At higher Landau-Levels we observe a
transport anisotropy that bears some similarity with what is already seen at
half-odd-integer filling on (001) oriented substrates. In addition we report
the first observation of transport anisotropies within the lowest Landau-Level.
This remarkable new anisotropy is independent of the current direction and
depends on the polarity of the magnetic field.Comment: 3 Pages, 4 figures, Latex, uses elsart.cls and physart.cls, to be
published in Physica E Added reference, made contact configuration more clea

### Central limit theorem for Hotelling's $T^2$ 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

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