Israel Journal of Mathematics

, Volume 147, Issue 1, pp 221–243 | Cite as

Compositions of random transpositions

  • Oded Schramm
Article

Abstract

LetY=(y1,y2, ...),y1≥y2≥..., be the list of sizes of the cycles in the composition ofcn transpositions on the set {1, 2, ...,n}. We prove that ifc>1/2 is constant andn → ∞, the distribution off(c)Y/n converges toPD(1), the Poisson-Dirichlet distribution with parameter 1, where the functionf is known explicitly. A new proof is presented of the theorem by Diaconis, Mayer-Wolf, Zeitouni and Zerner stating that thePD(1) measure is the unique invariant measure for the uniform coagulation-fragmentation process.

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Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  • Oded Schramm
    • 1
  1. 1.Microsoft ResearchRedmondUSA

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