  Motivated by the recent experimental observations of the DNA loop extrusion
by protein motors, in this paper we investigate the statistical properties of
the growing polymer loops within the ideal chain model. The loop conformation
is characterized statistically by the mean gyration radius and the pairwise
contact probabilities. It turns out that a single dimensionless parameter,
which is given by the ratio of the loop relaxation time over the time elapsed
since the start of extrusion, controls the crossover between near-equilibrium
and highly non-equilibrium asymptotics in statistics of the extruded loop.
Besides, we show that two-sided and one-sided loop extruding motors produce the
loops with almost identical properties. Our predictions are based on two
rigorous semi-analytical methods accompanied by asymptotic analysis of slow and
fast extrusion limits.
