Patrick Lopatto

Uniqueness of the mobility edge for Lévy matrices

We prove that the mobility edge equation introduced by Tarquini, Biroli, and Tarzia for Lévy matrices has a unique positive solution for every tail exponent $\alpha\in(0,1)$. Combined with a previous result by Aggarwal, Bordenave, and the author, this establishes for every $\alph...

Nearly-minimax variance estimation under rough random design

We identify the minimax exponent for constant conditional variance estimation under rough random design. The unknown design density is bounded above and away from zero, with no smoothness assumption, and the conditional error laws may depend on the covariates and have uniformly b...