5 papers
Unitary ensembles with a critical edge point, their multiplicative statistics and the Korteweg-de-Vries hierarchy
Mattia Cafasso, Carla Mariana da Silva Pinheiro
We study the multiplicative statistics associated to the limiting determinantal point process describing unitary random matrices with a critical edge point, where limiting density…
Multiplicative Averages of Plancherel Random Partitions: Elliptic Functions, Phase Transitions, and Applications
Mattia Cafasso, Matteo Mucciconi, Giulio Ruzza
We consider random integer partitions that follow the Poissonized Plancherel measure of parameter . Using RiemannHilbert techniques, we establish the asymptotics of th…
Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials
Mattia Cafasso, Ann du Crest de Villeneuve, Di Yang
For a simple Lie algebra and an irreducible faithful representation of , we introduce the Schur polynomials of -type. We then d…
Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations
Mattia Cafasso, Tom Claeys, Giulio Ruzza
We study a family of unbounded solutions to the Korteweg-de Vries equation which can be constructed as log-derivatives of deformed Airy kernel Fredholm determinants, and which are…
Biorthogonal measures, polymer partition functions, and random matrices
Mattia Cafasso, Tom Claeys
We develop the study of a particular class of biorthogonal measures, encompassing at the same time several random matrix models and partition functions of polymers. This general fr…