  While the structure of chromatin has been studied in great detail on length
scales below 30 nm, amazingly little is known about the higher-order folding
motifs of chromatin in interphase. Recent experiments give evidence that the
folding may depend locally on gene density and transcriptional activity and
show a leveling-off at long distances where approximately $<R^2> \sim O(1)$. We
propose a new model that can explain this leveling-off by the formation of
random loops. We derive an analytical expression for the mean square
displacement between two beads where the average is taken over the thermal
ensemble with a fixed but random loop configuration, while quenched averaging
over the ensemble of different loop configurations -- which turns out to be
equivalent to averaging over an ensemble of random matrices -- is performed
numerically. A detailed investigation of this model shows that loops on all
scales are necessary to fit experimental data.
