How Do Waves Propagate Randomness in Nature and Mathematical Models

Watch a 54-minute lecture exploring the complex dynamics of wave propagation and randomness in natural phenomena, delivered by Andrea Nahmod at the Simons Foundation. Delve into how waves manifest across various domains including quantum mechanics, fiber optics, ferromagnetism, atmospheric conditions, and water systems, examining their nonlinear interactions and inherent complexity. Learn about classical probability tools that provide frameworks for understanding wave dynamics through phase space ensembles rather than specific trajectories. Explore the paradigm shift in scaling that revealed random structures in nonlinear waves at high frequencies and fine scales. Discover how these concepts advanced the study of Gibbs measures in nonlinear Schrödinger equations and the hyperbolic Φ^4_3 model within equilibrium statistical mechanics and constructive quantum field theory. Conclude with an examination of current challenges in understanding long-term randomness propagation and out-of-equilibrium dynamics in wave systems.