# Random Matrix Theory and Gaussian Noise Thresholding

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This Demonstration shows an application of random matrix theory (RMT) to the problem of signal-from-noise separation in large real-valued symmetric random matrices that takes advantage of the RMT predictions about the nearest-neighbor spacing distribution (NNSD) between the eigenvalues of these matrices.

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Contributed by: Jessica Alfonsi (August 2020)

(Padova, Italy)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: structured block matrix with no Gaussian noise

Snapshot 2: eigenvalue spacing distribution computed from the matrix in Snapshot 1 following an exponential function

Snapshot 3: masked structured block matrix with superimposed Gaussian noise

Snapshot 4: eigenvalue spacing distribution computed from the matrix in Snapshot 3 following a Wigner surmise function (Gaussian orthogonal ensemble distribution)

This work was inspired by Uwe Menzel's introduction to his own authored R package detailed in [1, 2].

References

[1] U. Menzel. "RMThreshold: Signal-Noise Separation in Random Matrices by Using Eigenvalue Spectrum Analysis." (Aug 18, 2020) cran.r-project.org/web/packages/RMThreshold.

[2] U. Menzel. "RMThreshold: A Short Introduction." (Aug 18, 2020) www.matstat.org/content_en/RMT/RMThreshold_Intro.pdf.

## Permanent Citation