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

@article{Silverstein1979ONTR, title={ON THE RANDOMNESS OF EIGENVECTORS GENERATED FROM NETWORKS WITH RANDOM TOPOLOGIES}, author={Jack W. Silverstein}, journal={Siam Journal on Applied Mathematics}, year={1979}, volume={37}, pages={235-245} }

A model for the generation of neural connections at birth led to the study of W, a random, symmetric, nonnegative definite linear operator defined on a finite, but very large, dimensional Euclidean space [1]. A limit law, as the dimension increases, on the eigenvalue spectrum of W was proven, implying that realizations of W (being identified with organisms in a species) appear totally different on the microscopic level and yet have almost identical spectral densities.The present paper considers…

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For each n, let Un be Haar distributed on the group of n × n unitary matrices. Let xn,1, . . . ,xn,m denote orthogonal nonrandom unit vectors in C n and let un,k = (uk, . . . , u n k) ∗ = U∗ nxn,k, k…

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