| Abstract: |
| The local behavior of zeros of orthogonal polynomials depends on the local properties of the measure, and different universality classes correspond to different local behaviors. From a modern perspective, this is analyzed through the scaling limits of the Christoffel-Darboux kernel. Recent works have established necessary and sufficient conditions for the most studied universality classes, including bulk universality and hard-edge universality. In all these settings, the rescaled Christoffel-Darboux kernel converges to a single limit kernel.
In this talk, we introduce universality classes in which there is not a single limit kernel, but rather an entire cycle of limit kernels. We show that this type of behavior arises naturally from a fractal nature of the measure of orthogonality. |
|