  We study interaction-induced correlations in Luttinger liquid with multiple
Fermi edges. Many-particle correlation functions are expressed in terms of
Fredholm determinants ${\rm det}(1+\hat{A}\hat{B})$, where $A(\epsilon)$ and
$B(t)$ have multiple discontinuities in energy and time spaces. Such
determinants are a generalization of Toeplitz determinants with Fisher-Hartwig
singularities. We propose a general asymptotic formula for this class of
determinants and provide analytical and numerical support to this conjecture.
This allows us to establish non-equilibrium power-law singularities of
many-particle correlation functions. As an example, we calculate a two-particle
distribution function characterizing correlations between left- and
right-moving fermions that have left the interaction region.
