ArXiv discussion, talk by Vivek Singh

Friday 9 Oct 2026, 14:00 → 15:00 Europe/Stockholm

A92110 (Ångströmlaboratoriet )

Sofiya Sianiuta (Uppsala University)

Singh's talk: 

Title: A semiclassical Hilbert space for random matrix theory

 

Abstract:  In this talk, I will discuss the time evolution of thermal states in N×N random matrices at large-N. Taking inspiration from the chord Hilbert space construction in the double-scaled SYK model, I will argue that the Krylov basis provides a semiclassical Hilbert space description of these thermal states. For theories whose large-N spectral density is even and compactly supported with square-root edges, I will show that, under some additional analyticity conditions, the semiclassical Hamiltonian has the same asymptotic behavior at large Krylov depth as in double scaled SYK. Moreover, for a broad class of UV deformations of the DSSYK spectral density, which modify the spectrum at high energies while preserving the near edge behavior, the effective Hamiltonian in the Krylov basis reduces to the Liouville Hamiltonian of JT gravity in a low-energy continuum limit. This suggests that the semiclassical Hilbert space should be interpreted as the bulk Hilbert space of a dual gravitational description.