  We use recently introduced notion of stochastic soliton lattice for
quantitative description of soliton turbulence. We consider the stochastic
soliton lattice on a special band-gap scaling of the spectral surface of genus
$N$ so that the integrated density of states remains finite as $N \to \infty$
(thermodynamic type limit). We prove existence of the limiting stationary
ergodic process and associate it with the soliton turbulence. The phase space
of the soliton turbulence is a one-dimensional space with the random Poisson
measure. The zero density limit of the soliton turbulence coincides with the
Frish - Lloyd potential of the quantum theory of disordered systems.
