Large deviations for Hamiltonian systems: integrability vs resonances

by Mr Ricardo Grande (SISSA, Trieste, Italie)

Tuesday May 20, 2025, 2:00 PM → 3:00 PM Europe/Paris

Salle de séminaire (Orléans institut Denis Poisson)

Exposé décalé au séminaire de l'idp du jeudi 22 mai

Abstract: We study the formation of extreme waves from a statistical viewpoint in the context of various Hamiltonian systems. Firstly, we derive an asymptotic development for the probability of appearance of extreme waves as the amplitude of the wave tends to infinity. Secondly, we analyze the most likely mechanism of formation of such waves with the help of two toy models. 
In the case of an integrable Hamiltonian system, we show that extreme waves are typically the result of a linear superposition mechanism. In the case of a highly resonant system, however, we prove that a nonlinear focusing mechanism is most likely. This nonlinear mechanism is then proved to increase the likelihood of appearance of extreme waves, as has often been conjectured in the physics literature.