Mathematics Colloquia and Seminars

I'll describe an operator limit for a family of general beta ensembles which exhibit a double-scaling. In particular, a free parameter in the system provides for a cross-over between the more well-known soft" and "hard" edge point processes. Our new limit operator takes as input the Riccati diffusion associated with the Stochastic Airy Operator. This suggests a hierarchy of random operators analogous to the Painleve hierarchy observed at the level of correlation functions for double-scaling ensembles most widely studied at $\beta = 2$. Joint work with Jose Ramírez (Univ. Costa Rica).