  We argue that an ensemble of backgrounds best understands hydrodynamic
dispersion relations in a medium with few degrees of freedom and is therefore
subject to strong thermal fluctuations. In the linearized regime, dispersion
relations become describeable by polynomials with random coefficients. We give
a short review of this theory and perform a numerical study of the distribution
of the roots of polynomials whose coefficients are of the order of a Knudsen
series but fluctuate in accordance with canonical fluctuations of temperature.
We find that, remarkably, the analytic structure of the poles of fluctuating
dispersion relations is very different from deterministic ones, particularly
regarding the distribution of imaginary parts with respect to real components.
We argue that this provides evidence that hydrodynamic behavior persists, and
is enhanced, by non-perturbative background fluctuations.
