General-q KPZ scaling in Krylov dynamics

Establish analytically and numerically how KPZ scaling emerges for general deformation parameter q in the Krylov-basis dynamics of q-Gaussian or DSSYK-related systems, including the nature of the transition between Gaussian and KPZ regimes for finite and infinite-dimensional systems.

Background

The paper reports that KPZ scaling was previously identified in the formal q=1 limit using Hermite polynomials and Krylov-basis autocorrelators. With an artificial cutoff, the Gaussian-to-KPZ transition appeared as a third-order phase transition, whereas finite-dimensional systems exhibited a smooth crossover.

The corresponding analysis for general q is not provided in the paper and is explicitly deferred. This problem concerns determining whether the same scaling structure and transition behavior persist throughout the q-deformed setting.

References

A similar analytical and numerical analysis for general $q$ will be presented elsewhere .

— DSSYK, open ASEP/TASEP and 2d dilaton gravity at strong coupling  (2610.01790 - Gorsky et al., 1 Oct 2026) in Section 6, item 4, “Transition amplitudes on the Krylov chain”