<scp>Finite‐Rank</scp> Perturbations of Random Band Matrices via Infinitesimal Free Probability
<scp>Finite‐Rank</scp> Perturbations of Random Band Matrices via Infinitesimal Free Probability
We prove a sharp transition for the infinitesimal distribution of a periodically banded GUE matrix. For bandwidths , we further prove that our model is infinitesimally free from the matrix units and the normalized all‐1’s matrix. Our results allow us to extend previous work of Shlyakhtenko on finite‐rank perturbations of …