267 research outputs found
Exact Analytic Continuation with Respect to the Replica Number in the Discrete Random Energy Model of Finite System Size
An expression for the moment of partition function valid for any finite
system size and complex power is obtained for a simple spin
glass model termed the {\em discrete random energy model} (DREM). We
investigate the behavior of the moment in the thermodynamic limit using this expression, and find that a phase transition occurs at a
certain real replica number when the temperature is sufficiently low, directly
clarifying the scenario of replica symmetry breaking of DREM in the replica
number space {\em without using the replica trick}. The validity of the
expression is numerically confirmed.Comment: 31 pages, 8 eps figure
Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals
We provide a scheme for exploring the reconstruction limit of compressed
sensing by minimizing the general cost function under the random measurement
constraints for generic correlated signal sources. Our scheme is based on the
statistical mechanical replica method for dealing with random systems. As a
simple but non-trivial example, we apply the scheme to a sparse autoregressive
model, where the first differences in the input signals of the correlated time
series are sparse, and evaluate the critical compression rate for a perfect
reconstruction. The results are in good agreement with a numerical experiment
for a signal reconstruction.Comment: 6 pages, 3 figure
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