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Explore the mathematical foundations of Eulerian spontaneous stochasticity in this advanced lecture delivered at the Centre International de Rencontres Mathématiques. Delve into the phenomenon where stochastic classical equations with vanishing randomness and singular dynamics converge to probability measures over non-unique weak solutions of deterministic systems. Examine how Edward Lorenz's 1969 work on turbulent flow predictability anticipated this concept, and understand its connection to the convex integration studies by De Lellis, Székelyhidi, and others that revealed infinitely many non-unique admissible weak solutions for Euler equations. Learn about the universal nature of limiting probability measures that provide well-posed solutions to Cauchy problems for deterministic dynamics, and discover how this framework illuminates Lorenz's pioneering contributions to turbulence theory. Gain insights into the mathematical rigor behind spontaneous stochasticity as it applies to Eulerian descriptions of fluid dynamics, building upon the foundational concepts of stochastic limits in singular dynamical systems.
