发表刊物：Submitted

摘要：We study the transition asymptotics of Toeplitz determinants with symbols \(f_{t}\) depending on a parameter $t$ where \(f_{t}\) has three Fisher-Hartwig singularities when \(t>0\) and two Fisher-Hartwig singularities when $t=0$. Using the Riemann-Hilbert approach to orthogonal polynomials, we establish double scaling limits where \(n \to \infty\) and simultaneously \(t \to 0\), and express the transition in terms of Painlevé transcendents. The results extend previous analysis of merging singularities and highlight a new type of Fisher–Hartwig transition on the unit circle. As an application, we study gap probability for thinned Circle Unitary Ensemble with an external potential.

合写作者：Pan Ma, Xuanzhuo Zhou

论文类型：期刊论文

学科门类：理学

一级学科：数学

文献类型：J

是否译文：否