An Integral Characterization of Random Permutations. A Point Process Approach

摘要

We consider random finite permutations and prove the following version of Thoma's theorem in [8]: Random finite permutations which are class functions satisfy a new integration by parts formula if and only if they are given by a certain Ewens-Siito process. The main source of inspiration for the results in this note is the fundamental work of Andras Siito [7], from which some results are reestablished here again in the present point process approach.