Fig. 5.

Eigenvalue spectrum of $n=200$ fingerprints of length $p=50$ sampled from $P\left(\lambda \right)$ in Eq. 5, with $w=0$ and $J=-\alpha {\mathbf{u\prime }}_{\mathbf{J}}{\mathbf{u}}_{\mathbf{J}}$ a rank-1 matrix described in the text. (A) The spectrum with $\beta \hspace{0.17em}\alpha =0.1$ agrees quantitatively with the MP distribution (red line). At high temperature the covariance structure of J is irrelevant and the fingerprints are uncorrelated up to sampling noise. (B) The spectrum with $\beta \hspace{0.17em}\alpha =0.6$ has a bulk that agrees with the MP distribution (red line), but has a single eigenvalue escape from the bulk, near $\lambda \approx 9$. (C) The eigenvector $\mathbf{v}$ associated with this eigenvalue is highly correlated with ${\mathbf{u}}_{\mathbf{J}}$, the direction of J.