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Abstract: We investigate the macroscopic behaviour of the density fluctuations of a one dimensional dynamics of hard rods with random length. After recentering on the effective velocity (hyperbolic space-time scaling) the density fluctuations of particles of a given velocity v will evolve on the diffusive scaling driven by a browian motion with a diffusivity depending on v. This rigid evolution of fluctuations is expected in other completely integrable systems (Box-Ball, Toda Lattice,..), in contrast with the behavior expected in chaotic dynamics.
Joint work with Pablo Ferrari (U. Buenos Aires).