114,660 research outputs found
Central limit theorem for signal-to-interference ratio of reduced rank linear receiver
Let with
independent and identically distributed complex random
variables. Write ,
and
. Define
$\beta_{km}=p_k\mathbf{s}_k^*\mathbf{A}_{km}(\mathbf {A}_{km}^*\times\
mathbf{R}_k\mathbf{A}_{km})^{-1}\mathbf{A}_{km}^*\mathbf{s}_kkN/K\to c>0$. 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
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
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