In reduced BMN matrix models, Lanczos coefficients scale linearly with the mass parameter, producing quadratic corrections to early-time Krylov complexity growth at the same order for both state and operator versions.
Tridiagonalizing random matrices,
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An analytical method is presented to calculate Lanczos coefficients governing Krylov complexity in the reduced pulsating fuzzy sphere version of the BMN matrix model for large and small deformations.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.