We lo ok at various measures on partitions coming from combinatorial representat ion theory: the so-called Schur measures and some variants. We are interes ted in fluctuations of the largest part(s) of said partitions --- discrete versions of largest eigenvalues of random matrices. One gets the Airy 2 ( Tracy--Widom) fluctuations in the original Schur measure corresponding to the Baik--Deift--Johansson longest increasing subsequences theorem\; Airy 1 (GOE) and GSE fluctuations for random involutions (Baik--Rains\; Ferrari \; Imamura--Sasamoto\; Baik--Barraquand--Corwin-- Suidan\; Betea--Bouttier --Nejjar--Vuletic\; Bisi--Zygouras)\; Airy 2 to 1 (along with a certain du al) fluctuations for symplectic and orthogonal Schur measures recently stu died by the author and for a related model of Bisi--Zygouras\; and finally finite temperature Airy2/Tracy--Widom fluctuations (interpolating between Gumbel and regular Tracy--Widom\; between Edwards--Wilkinson and KPZ) for a certain '\;cylindric'\; version of the Baik--Deift--Johansson cas e (joint work of the author and Jeremie Bouttier). All such measures can b e treated uniformly with the aid of fermionic Fock space (equivalently\, t hey are determinantal processes)\, as was first championed by Okounkov. Mo st if not all results relate to last passage percolation problems in certa in simple geometries. All results are inspired by and have continuous rand om matrix analogues. It is conjectured though remains unproven that each A iry-type distribution described above is universal for the geometry in que stion: the so-called KPZ universality.

LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS T Austria ORGANIZER:jdeanton@ist.ac.at SUMMARY:Integrable measures on partitions and Airy limit processes URL:https://talks-calendar.app.ist.ac.at/events/1245 END:VEVENT END:VCALENDAR