# Spectral Analysis of Networks with Random Topologies

@article{Grenander1977SpectralAO, title={Spectral Analysis of Networks with Random Topologies}, author={Ulf Grenander and Jack W. Silverstein}, journal={Siam Journal on Applied Mathematics}, year={1977}, volume={32}, pages={499-519} }

A class of neural models is introduced in which the topology of the neural network has been generated by a controlled probability model. It is shown that the resulting linear operator has a spectral measure that converges in probability to a universal one when the size of the net tends to infinity: a law of large numbers for the spectra of such operators. The analytical treatment is accompanied by omputational experiments.

## 83 Citations

### ON THE RANDOMNESS OF EIGENVECTORS GENERATED FROM NETWORKS WITH RANDOM TOPOLOGIES

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- 1995

A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marcenko and Pastur, is presented. Here, X(N - n), T(n - n),…

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