Geodesic
Spectral criterion for testing hypotheses on random permutations
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 3, pp. 19-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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Suppose that for each of $N$ independent identically distributed random permutations we observe a pair consisting of a random uniformly distributed argument and a corresponding value of permutation. We consider the problem of testing the hypothesis that the distribution of permutations is uniform against the hypothesis that permutations are the products of r independent permutations with known distribution. A test constructed by eigenvectors of matrices of transition probabilities (arguments to values) is proposed and investigated. 
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O. V. Denisov. Spectral criterion for testing hypotheses on random permutations. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 3, pp. 19-28. http://geodesic.mathdoc.fr/item/MVK_2016_7_3_a1/

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