  We consider spatial coarse-graining in statistical ensembles of
non-selfintersecting and one-fold selfintersecting center-vortex loops as they
emerge in the confining phase of SU(2) Yang-Mills thermodynamics. This
coarse-graining is due to a noisy environment and described by a curve
shrinking flow of center-vortex loops locally embedded in a two-dimensional
flat plane. The renormalization-group flow of an effective `action', which is
defined in purely geometric terms, is driven by the curve shrinking evolution.
  In the case of non-selfintersecting center-vortex loops, we observe critical
behavior of the effective `action' as soon as the center-vortex loops vanish
from the spectrum of the confining phase due to curve shrinking. This suggest
the existence of an asymptotic mass gap.
  An entirely unexpected behavior in the ensemble of one-fold selfintersecting
center-vortex loops is connected with the spontaneous emergence of order. We
speculate that the physics of planar, one-fold selfintersecting center-vortex
loops to be relevant for two-dimensional systems exhibiting high-temperature
superconductivity.
