Logarithmic Spectral Edge Growth in Random Hankel Trajectory Matrices

We prove that the largest eigenvalue of the trajectory covariance matrix constructed from white noise via Hankel delay embedding grows logarithmically with the embedding dimension. The mechanism arises from a Fejér-squared overlap geometry that induces weakly dependent Fourier Rayleigh quotients, whose extreme-value statistics produce the logarithmic edge. We also establish structural results for sinusoidal and autoregressive signals.