  We investigate the statistics of rogue waves occurring in the inverse cascade
of surface gravity wave turbulence. In such statistically homogeneous,
stationary and isotropic wave fields, low-frequency waves are generated by
nonlinear interactions rather than directly forced by a wave maker. This
provides a laboratory realization of arguably the simplest nonlinear sea state,
in which long-time acquisitions are performed and compared with theoretical
models. The analysis of thousands of rogue waves reveals that some of their
properties crucially depend on four-wave resonant interactions, large crests
being for instance more likely than predicted by second-order models.
