Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 26 mars 2019 à 14h00 en B107, Dan Betea nous parlera de : From Gumbel to Tracy--Widom II, via integer partitions

Résumé : There are two natural well-studied measures on integer partitions: Plancherel and uniform. In the scaling limit, their first parts behave differently and on a different scale: Plancherel shows random matrix-type Tracy-Widom statistics (the Baik-Deift-Johansson theorem), while uniform shows Gumbel, a maximum of independent Gaussians (the Erdős-Lehner theorem). In this talk, based on joint work with Jérémie Bouttier, we present the 'finite temperature/cylindric' extension of the Plancherel measure, coming from counting standard Young tableaux of skew shape and interpolating between Plancherel and uniform. The edge scaling limit yields the finite temperature Tracy-Widom distribution of Johansson, observed in random matrix models and interpolating between Tracy-Widom and Gumbel statistics. A time-extension of the result yields the finite temperature/periodic extended Airy process of Le Doussal-Majumdar-Schehr.


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