Publication at Faculty of Mathematics and Physics |
2023
Abstract
The Freud ensemble of random matrices is the unitary invariant ensemble corresponding to the weight exp(-n vertical bar x vertical bar(beta)), beta > 0, on the real line. We consider the local behaviour of eigenvalues near zero, which exhibits a transition in beta.
If beta >= 1, it is described by the standard sine process. Below the critical value beta = 1, it is described by a process depending on the value of beta, and we determine the first two terms of the large gap probability in it.
This so called weak confinement range 0 = 1.