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The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally treelike, and sparse covariance matrices. We derive a closed set of equations from which the density of eigenvalues can be efficiently calculated. Within this approach, the(More)
We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L<inf>1</inf>-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix modeled as the Kronecker-type random matrix studied in research on multiple-input multiple-output wireless(More)
{ An approach to analyze the performance of the code division multiple access (CDMA) scheme, which is a core technology used in modern wireless communication systems, is provided. The approach characterizes the objective system by the eigenvalue spectrum of a cross-correlation matrix composed of signature sequences used in CDMA communication, which enable(More)
PACS 89.70.-a – Information and communication theory PACS 75.10.Nr – Spin-glass and other random models PACS 05.70.Fh – Phase transitions: general studies Abstract.-We provide a scheme for exploring the reconstruction limits of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correlated signal(More)
The Kronecker channel model of wireless communication is analyzed using statistical mechanics methods. In the model, spatial proximities among transmission/reception antennas are taken into account as certain correlation matrices, which generally yield non-trivial dependence among symbols to be estimated. This prevents accurate assessment of the(More)
A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in Europhys. Lett., 76 (2006) 1193 and enables the analysis of the system in which the elements of the channel transfer(More)
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We study the decay process of an unstable quantum system, especially the deviation from the exponential decay law. We show that the exponential period no longer exists in the case of the s-wave decay with small Q value, where the Q value is the difference between the energy of the initially prepared state and the minimum energy of the continuous eigenstates(More)