  Strongly correlated transport of interacting electrons through the
one-dimensional tunnel contact is considered within the Luttinger liquid model
of one-dimensional electrodes on arbitrary time scales $ t> \hbar /\Lambda_{g}
$. Using previous results, namely, the Self-equilibration theorem proven in
Ref.[G.Skorobagatko, Ann.Phys., 422, 168298 (2020)] the exact distribution
functions $ P(N,t) $ for the probabilities of $ N $ electrons to tunnel through
the contact during the fixed time interval $ t $ are derived and plotted as 3D
intensity graphs called real-time tunneling maps in a whole available region of
Luttinger liquid correlation parameter values, bias voltages, and temperatures.
The tunneling maps being obtained reveal tunneling anomalies -unusually high
tunneling probabilities for the small numbers of electrons on the short-time
scales beyond the steady state regime of electron tunnel transport. Especially,
this concerns the case of strong short-range electron-electron interaction in
the leads at $ g \lesssim 1/2 $. The effect being found can be treated as the
direct consequence of the self-equilibration phenomenon. It is shown that
features of such an anomalous electron tunneling beoynd the steady state regime
can be used for precise experimental measurements of small differences between
Luttinger liquid correlation parameter values in different one-dimensional
quantum-point contacts.
