Currents in the thermal Toda lattice have space-time fluctuations converging to an explicit Gaussian process under diffusive scaling, implying Brownian motion for particle positions and inverse-time decaying correlations.
Teschl.Jacobi operators and completely integrable nonlinear lattices, volume 72 ofMathematical Surveys and Monographs
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Fluctuations for the Toda lattice
Currents in the thermal Toda lattice have space-time fluctuations converging to an explicit Gaussian process under diffusive scaling, implying Brownian motion for particle positions and inverse-time decaying correlations.