Universal edge scaling in random partitions

Taro Kimura (1) , Ali Zahabi (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We establish the universal edge scaling limit of random partitions with the infinite-parameter distribution called the Schur measure. We explore the asymptotic behavior of the wave function, which is a building block of the corresponding kernel, based on the Schrödinger-type differential equation. We show that the wave function is in general asymptotic to the Airy function and its higher-order analogs in the edge scaling limit. We construct the corresponding higher-order Airy kernel and the Tracy-Widom distribution from the wave function in the scalins limit, and discuss its implication to the multicritical phase transition in the large size matrix model. We also discuss the limit shape of random partitions through the semi-classical analysis of the wave function.

Mots clés: wave function: asymptotic behavior; scaling; higher-order; differential equations; critical phenomena; matrix model; Schroedinger equation

Domaines: Physique Générale [physics.gen-ph]; Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

Taro Kimura, Ali Zahabi. Universal edge scaling in random partitions. Letters in Mathematical Physics, 2021, 111 (2), pp.48. ⟨10.1007/s11005-021-01389-y⟩. ⟨hal-03229406⟩