Let sk=N1(v1k,...,vNk)T, with
{vik,i,k=1,...} independent and identically distributed complex random
variables. Write Sk=(s1,...,sk−1,sk+1,...,sK),Pk=diag(p1,...,pk−1,pk+1,...,pK),
Rk=(SkPkSk∗+σ2I) and
Akm=[sk,Rksk,...,Rkm−1sk]. Define
$\beta_{km}=p_k\mathbf{s}_k^*\mathbf{A}_{km}(\mathbf {A}_{km}^*\times\
mathbf{R}_k\mathbf{A}_{km})^{-1}\mathbf{A}_{km}^*\mathbf{s}_k,referredtoasthesignal−to−interferenceratio(SIR)ofuserkunderthemultistageWiener(MSW)receiverinawirelesscommunicationsystem.ItisprovedthattheoutputSIRundertheMSWandthemutualinformationstatisticunderthematchedfilter(MF)arebothasymptoticGaussianwhenN/K\to c>0$. 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
'Bernoulli Society for Mathematical Statistics and Probability'
Publication date
01/01/2012
Field of study
Let Xp=(s1,...,sn)=(Xij)p×n
where Xij's are independent and identically distributed (i.i.d.) random
variables with EX11=0,EX112=1 and EX114<∞. It is showed
that the largest eigenvalue of the random matrix
Ap=2np1(XpXp′−nIp)
tends to 1 almost surely as p→∞,n→∞ with
p/n→0.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
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