  A statistical theory of rogue waves is proposed and tested against
experimental data collected in a long water tank where random waves with
different degrees of nonlinearity are mechanically generated and free to
propagate along the flume. Strong evidence is given that the rogue waves
observed in the tank are hydrodynamic instantons, that is, saddle point
configurations of the action associated with the stochastic model of the wave
system. As shown here, these hydrodynamic instantons are complex
spatio-temporal wave field configurations, which can be defined using the
mathematical framework of Large Deviation Theory and calculated via tailored
numerical methods. These results indicate that the instantons describe equally
well rogue waves that originate from a simple linear superposition mechanism
(in weakly nonlinear conditions) or from a nonlinear focusing one (in strongly
nonlinear conditions), paving the way for the development of a unified
explanation to rogue wave formation.
