  We examine numerically the full spatio-temporal correlation functions for all
hydrodynamic quantities for the random collision model introduced recently. The
autocorrelation function of the heat current, through the Kubo formula, gives a
thermal conductivity exponent of 1/3 in agreement with the analytical
prediction and previous numerical work. Remarkably, this result depends
crucially on the choice of boundary conditions: for periodic boundary
conditions (as opposed to open boundary conditions with heat baths) the
exponent is approximately 1/2. This is expected to be a generic feature of
systems with singular transport coefficients. All primitive hydrodynamic
quantities scale with the dynamic critical exponent predicted analytically.
