  The notion of Thouless energy plays a central role in the theory of Anderson
localization. We investigate the scaling of Thouless energy across the
many-body localization (MBL) transition in a Floquet model. We use a
combination of methods that are reliable on the ergodic side of the transition
(e.g., spectral form factor) and methods that work on the MBL side (e.g.
typical matrix elements of local operators) to obtain a complete picture of the
Thouless energy behavior across the transition. On the ergodic side, the
Thouless energy tends to a value independent of system size, while at the
transition it becomes comparable to the level spacing. Different probes yield
consistent estimates of the Thouless energy in their overlapping regime of
applicability, giving the location of the transition point nearly free of
finite-size drift. This work establishes a connection between different
definitions of Thouless energy in a many-body setting, and yields new insights
into the MBL transition in Floquet systems.
