论文标题
具有单切正规电位和Fisher的toeplitz决定因素 - hartwig奇异性I.单位圆支撑的平衡度量
Toeplitz determinants with a one-cut regular potential and Fisher--Hartwig singularities I. Equilibrium measure supported on the unit circle
论文作者
论文摘要
我们考虑具有符号具有的toeplitz决定因素：（i）一个定期的潜在$ V $，（ii）Fisher- hartwig奇异性，以及（iii）背景中的平滑功能。潜在的$ V $与假定在整个单元圆上支持的平衡度量有关。对于恒定电势$ V $，平衡度量是单位圆的均匀度量，我们的公式将Fisher-Hartwig奇异性的Toeplitz决定因素降低为已知的结果。对于非恒定$ v $，即使没有Fisher-Hartwig奇异性，我们的结果似乎也是新的。作为结果的应用，我们得出了确定点过程的各种统计特性，该过程概括了圆形单一合奏。
We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential $V$, (ii) Fisher--Hartwig singularities, and (iii) a smooth function in the background. The potential $V$ is associated with an equilibrium measure that is assumed to be supported on the whole unit circle. For constant potentials $V$, the equilibrium measure is the uniform measure on the unit circle and our formulas reduce to well-known results for Toeplitz determinants with Fisher--Hartwig singularities. For non-constant $V$, our results appear to be new even in the case of no Fisher--Hartwig singularities. As applications of our results, we derive various statistical properties of a determinantal point process which generalizes the circular unitary ensemble.
