Brian Rider (Temple Unversity)
罢颈迟濒别:听A matrix model for conditioned Stochastic Airy.
Abstract:聽There are three basic flavors of local limit theorems in random matrix theory, connected to the spectral bulk and the so-called soft and hard edges. There also abound a collection of more exotic limits which arise in models that posses degenerate (or 鈥渘on-regular鈥�) points in their equilibrium measure. 聽What is more, there is typically a natural double scaling about these non-regular points, producing limit laws that transition between the more familiar basic flavors. Here I will describe a general beta matrix model for which,听肠辞苍箩别肠迟耻谤补濒濒测, the appropriate double scaling limit is the Stochastic Airy Operator, conditioned on having no eigenvalues below a fixed level. 聽This is work in progress with J. Ramirez (University of Costa Rica). I will be honest as to what aspects remain conjectural.