Cyclization is process whereby one end of DNA comes into contact with the other end of the same strand and the two ends have the same orientation. If DNA ligase is present then then the DNA can be glued into a circle at a rate dependent on the cyclization J-factor (proportional to the probability density).
Here we plot the J factor as a function of length for wormlike chain DNA, as computed using the Gaussian chain model and the much more accurate eigenfunction expression of Spakowitz and Wang. Clearly the Gaussian chain model only works when the DNA is long relative to the persistence length -- longer than the segments we have tested here. The true form of the J factor drops off at short lengths (due to a large energetic penalty of bending the DNA sharply) and at long lengths (due to the entropic difficulty of having the two ends find one another), and is modulated at the helical repeat length of 10.5 bp owing to the twist constraint.