Rogue Waves and Large Deviations for the 2D Pure Gravity Deep Water Wave Equations

Explore the mathematical analysis of rogue waves through this 56-minute conference talk that rigorously examines extreme ocean events characterized by sudden formation of anomalously large crests. Delve into the quantification of probability for rogue wave formation under random Gaussian sea initial data, focusing on the pure gravity water wave equations in deep water. Learn how the research justifies the exponential large-tail law probability for rogue wave formation up to optimal timescales allowed by deterministic well-posedness theory. Discover the proof mechanism showing that rogue waves most likely arise through "dispersive focusing," where phase synchronization produces constructive amplification of water crests. Understand the main challenge of propagating statistical information over long timescales and how it's overcome by combining normal forms and probabilistic methods. Examine this novel approach that, unlike previous results, does not require approximate solutions to be Gaussian, representing joint work with M. Berti, R. Grande and A. Maspero in the intersection of oceanography and advanced mathematical analysis.