Guilherme Silva

Multiplicative statistics for random matrices and the integro-differential Painlevé II

It has been known since the 1990s that fluctuations of eigenvalues of random matrices, when appropriately scaled and in the sense of one-point distribution, converge to the Airy2 point process in the large matrix limit. In turn, the latter can be described by the celebrated Tracy-Widom distribution. In this talk we discuss recent findings of Promit Ghosal and myself, showing that certain statistics of eigenvalues also converge universally to appropriate statistics of the Airy2 point process, interpolating between a hard and soft edge of eigenvalues. Such found statistics connect also to the integro-differential Painlevé II equation, in analogy with the celebrated Tracy-Widom connection between Painlevé II and the Airy2 process, and also indicate an interplay between the KPZ equation and random matrices.

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/f1498504c1df4162bd42f8f7c40556901d