Spectral topology, meaning the gap structure of the support, refines the universal classification of Krylov operator growth: gaps produce quasiperiodic Lanczos coefficients, and a gap closing with a double density zero gives a Painleve-governed n^{-1/3} transition.
Widom,Extremal polynomials associated with a system of curves in the complex plane,Advances in Mathematics3(1969) 127
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Spectral Topology and Universal Krylov Dynamics
Spectral topology, meaning the gap structure of the support, refines the universal classification of Krylov operator growth: gaps produce quasiperiodic Lanczos coefficients, and a gap closing with a double density zero gives a Painleve-governed n^{-1/3} transition.