Geodesic
Subordinators and the actions of permutations with quasi-invariant measure
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Tome 223 (1995), pp. 181-218 
S. V. Kerov. Subordinators and the actions of permutations with quasi-invariant measure. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Tome 223 (1995), pp. 181-218. http://geodesic.mathdoc.fr/item/ZNSL_1995_223_a10/
@article{ZNSL_1995_223_a10,
     author = {S. V. Kerov},
     title = {Subordinators and the actions of permutations with quasi-invariant measure},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {181--218},
     year = {1995},
     volume = {223},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_223_a10/}
}
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We introduce a class of probability measures in the space of virtual permutations associated with subordinators (i.e., processes with stationary positive independent increments). We prove that these measures are quasi-invariant under both left and right actions of the countable symmetric group $\mathfrak S_\infty$, and a simple formula for the corresponding cocycle is obtained. In case of a stable subordinator, we find the value of the spherical function of a constant vector on the class of transpositions. Bibliography: 19 titles.