  We summarize results on the asymptotics of the two-particle Green functions
of interacting electrons in one dimension. Below a critical value of the
chemical potential the Fermi surface vanishes, and the system can no longer be
described as a Luttinger liquid. Instead, the non-relativistic Fermi gas with
infinite point-like repulsion becomes the universal model for the
long-wavelength, low temperature physics of the one-dimensional electrons. This
model, which we call the impenetrable electron gas, allows for a rigorous
mathematical treatment. In particular, a so-called determinant representation
for the two particle Green function could be derived. This determinant
representation is related to an integrable classical evolution equation and to
a Riemann-Hilbert problem, that enable the exact calculation of the asymptotics
of the two-particle Green functions.
