Random matrix theory for complexity growth and black hole interiors

We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual Jackiw-Teitelboim gravity two-dimensional conformal field theories. This is refined, "microcanonical" version K-complexity that applies to theories with infinite or continuous spectra (including theories), we exhibits exponential growth for scrambling time, followed by linear until saturation at time entropy $\unicode{x2014}$a behavior characteristic chaos. show regime implies universal random matrix description dynamics after scrambling. Our main tool establishing this connection "complexity renormalization group" framework develop allows us effective different timescales "integrating out" large K-complexities. In setting, comment on empirical match between our maximal volume proposal, speculate theory spatial translation symmetry smooth black hole interiors.