报 告 人：李韫 博士
报告题目: Edge imits of the truncated circular beta ensembles
Consider the circular unitary ensemble with the first row and column deleted, the resulting model is sub-unitary with eigenvalues lying inside the unit disk. Zyczkowski and Sommers derived the joint eigenvalue distribution of a truncated circular unitary ensemble, and showed they form a determinantal point process. Taking the limit of these points (without any additional scaling) one obtains the zeros of the Gaussian analytic function studied by Peres and Virag.
Killip and Kozhan provided a random matrix model that can be considered as the truncated circular beta ensemble (with beta = 2 corresponding to the unitary case), and described the spectrum via a random recursion. We derive and describe the point process limit of the truncated circular beta ensemble (near 1) together with the scaling limit of the normalized characteristic polynomials. We also treat multiplicative rank one perturbation of the models. The limiting objects are closely connected to the random analytic function appearing as the limit of the normalized characteristic polynomials of the (full) circular beta ensemble. Based on joint work with Benedek Valko.