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.

Dernière modification : Monday 27 May 2024

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr