Seminar
RANDOM PARTITIONS ON THE EDGE. THE AIRY ZOO
by DAN BETEA (KU Leuven)
Location: 200B.02.18, Leuven
Time: Tuesday December 10, 2019 at
14:00
We describe edge scaling of various measures on random partitions, motivated by combinatorics and statistical mechanics. The results yield a zoo of Airy processes appears: the Airy 2 process and the Tracy–Widom GUE distribution, the Airy 1 process and the GOE distribution, the Airy 2-to-1 process, Johansson’s finite temperature Airy process and the corresponding finite temperature distribution generalizing Tracy–Widom GUE, analogues of the latter generalizing the GOE/GSE distributions, a half-space generalization of the Baik–Rains distribution, etc. The techniques used for the proofs are: a bit of algebraic combinatorics and representation theory, determinantal point processes and/through free fermions, (mild) special function techniques, and classical steepest descent analysis. The bulk of the talk is based on joint work with (subsets of) {Jérémie Bouttier, Patrik Ferrari, Peter Nejjar, Alessandra Occelli, and Mirjana Vuletić}.
