Static Model

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 17)


Since the Plancherel measure on the path space of the Young graph is ergodic, some deterministic aspects will appear in a macroscopic point of view. In this chapter, we describe the famous limit shape problem for the profiles of random Young diagrams in the Plancherel ensemble, which is due to Vershik–Kerov and Logan–Shepp, as a strong law of large numbers for the Plancherel measure on the path space. Free cumulants of the transition measure play a central role in characterizing the limit shape of Young diagrams.


Probability Space Young Diagram Irreducible Character Tracial State Path Space 

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© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan

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