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A New Approach to Universality Limits involving Orthogonal Polynomials
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We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure mu on [-1,1]. Assume that mu is a regular measure, and is absolutely continuous in an open interval containing some closed subinterval J of (-1,1). Assume that in J, the absolutely continuous component mu' is positive and continuous. Then universality in J for mu follows from universality for the classical Legendre weight. We also establish universality in an L_{p} sense under weaker assumptions on mu.
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Krylov Distribution and Universal Convergence of Quantum Fisher Information
A spectral-resolvent Krylov framework defines a distribution for quantum Fisher information and identifies universal exponential or algebraic convergence regimes based on the Liouville spectrum.
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