We use the recently introduced notion of stochastic soliton lattice for qua
ntitative description of soliton turbulence. We consider the stochastic sol
iton 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 --> infinit
y (thermodynamic type limit). We prove existence of the limiting stationary
ergodic process and associate it with the homogeneous soliton turbulence.
The phase space of the soliton turbulence is a one-dimensional space with t
he random Poisson measure. The zero-density limit of the soliton turbulence
coincides with the Frish-Lloyd potential of the quantum theory of disorder
ed systems. (C) 2001 Published by Elsevier Science B.V.