论文标题
自由场和Verblunsky系数的S^1痕迹的指数
The Exponential of the S^1 Trace of the Free Field and Verblunsky Coefficients
论文作者
论文摘要
Szego的身份和音量计算，启发式上暗示了Verblunsky系数相对于高斯自由场的$ s^1 $跟踪的（归一化）指数的简单表达。这种启发式表达不是完全正确的。 Chhaibi和Najnudel发现了正确公式的证明。他们的证明使用随机矩阵理论，并克服了许多困难的技术问题。除了呈现Szego的观点外，我们还表明，Chhaibi和Najnudel定理暗示了一个组合身份（对于措施时刻）具有内在兴趣。
An identity of Szego, and a volume calculation, heuristically suggest a simple expression for the distribution of Verblunsky coefficients with respect to the (normalized) exponential of the $S^1$ trace of the Gaussian free field. This heuristic expression is not quite correct. A proof of the correct formula has been found by Chhaibi and Najnudel. Their proof uses random matrix theory and overcomes many difficult technical issues. In addition to presenting the Szego perspective, we show that the Chhaibi and Najnudel theorem implies a family of combinatorial identities (for moments of measures) which are of intrinsic interest.
