Speaker: 李韫, 清华大学

Inviter: 随机分析研究中心

Title: Limits of the truncated circular beta ensembles

Language: Chinese

Time & Venue: 2025.10.10 16:00-17:00 南楼613

Abstract: Consider a Haar unitary matrix with the first row and column deleted, Zyczkowski and Sommers derived the joint distribution of the eigenvalues, and showed that they form a determinantal point process. Killip and Kozhan extended this result to circular beta ensembles, and provided a description of the spectrum of the truncated version of the circular beta ensembles (with beta=2 corresponding to the Haar unitary case). In this talk, I will discuss the edge and bulk point process limits of the truncated circular beta ensembles, along with the scaling limits of the normalized characteristic polynomials. The limiting objects are closely connected to the stochastic zeta function and the iid Gaussian power series in the edge and bulk regimes, respectively. I will also explain how the random Dirac-type operator framework can be used to derive scaling limits for the full and truncated circular ensembles. Based on joint works with Mingchang Liu, Joseph Najnudel, and Benedek Valko.