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We consider random permutations derived by sampling from stick-breakingpartitions of the unit interval. The cycle structure of such a permutation canbe associated with the path of a decreasing Markov chain on $n$ integers. Undercertain assumptions on the stick-breaking factor we prove a central limittheorem for the logarithm of the order of the permutation, thus extending theclassical Erd\H{o}s-Tur\'an law for the uniform permutations and itsgeneralization for Ewens' permutations associated with sampling from thePD/GEM$(\theta)$ distribution. Our approach is based on using perturbed randomwalks to obtain the limit laws for the sum of logarithms of the cycle lengths.

A generalization of the Erd\H{o}s-Tur\'an law for the order of random permutation