S.V.Kerov and N.V.Tsilevich.
Stick breaking process generates virtual permutations with Ewens distribution.
Zapiski Nauchn. Semin. POMI, 223 (1995), 162-180.
English translation: J. Math. Sci. (N.Y.), 87, No. 6 (1997), 4082-4093.

Abstract. Given a sequence $x$ of points in the unit interval, we associate with it a virtual permutation $w=w(x)$ (that is, a sequence $w$ of permutations $w_n \in \frak S_n$ such that $w_{n-1}=w_n'$ is obtained from $w_n$ by erasing the last element $n$ from its cycle, for all $n=1,2,\,\ldots$). We introduce a detailed version of the well-known stick breaking process, generating a random sequence $x$. It is proved that the associated random virtual permutation $w(x)$ has Ewens' distribution. Up to subsets of zero measure, the space $\frak S^\infty = \varprojlim \frak S_n$ of virtual permutations is identified with the cube $[0,1]^\infty$.

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