Compositions of random transpositions
نویسنده
چکیده
Let Y = (y1, y2, . . . ), y1 ≥ y2 ≥ · · · , be the list of sizes of the cycles in the composition of c n transpositions on the set {1, 2, . . . , n}. We prove that if c > 1/2 is constant and n → ∞, the distribution of f(c)Y/n converges to PD(1), the Poisson-Dirichlet distribution with paramenter 1, where the function f is known explicitly. A new proof is presented of the theorem by Diaconis, Mayer-Wolf, Zeitouni and Zerner stating that the PD(1) measure is the unique invariant measure for the uniform coagulation-fragmentation process.
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