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math.PR2026
An Exact Tail Condition for the Largest Error in Estimating a Rank-One Direction
Guilherme Vianna
We consider a rectangular random matrix formed by adding a rank-one term to a matrix with independent entries. The direction on the left side of that term is estimated by the leadi…
math.PR2026
Hard-Edge Determinant Fields and Second-Moment Universality for Random Matrix Ratios
Guilherme Vianna
We study the microscopic spectrum at the origin of ratios of independent complex Girko matrices. Under bounded-density and finite-moment assumptions, together with circular second-…