= Solution
At criticality, <percolation clusters> occur on every scale. Count their filled outer perimeters, discard microscopic loops through a diameter cutoff, and then pass to a <scaling limit>. The cutoff gives a locally finite measure on loops of macroscopic size inside a bounded region; summing over scales gives a <sigma-finite measure> rather than a probability distribution.
The <conformal invariance of planar percolation> makes these limiting perimeter statistics covariant under <conformal maps>. Moreover, deciding whether a filled outer perimeter lies in a simply connected subdomain uses only the configuration it encloses: changing the configuration outside that subdomain does not change that perimeter. This is the restriction part of the argument. Conformal <covariance> together with this domain consistency motivates a nonzero <conformal restriction measure on simple loops>.
This is an informal construction principle, as requested; it does not replace the tightness, boundary-simplification and uniqueness theorems required to construct the continuum measure rigorously.
Back to article page
