论文标题
通过大偏差的总和规则：扩展到多项式电位和多切割机制
Sum rules via large deviations: extension to polynomial potentials and the multi-cut regime
论文作者
论文摘要
总和规则是将量度的熵与与其正交多项式构建有关的系数（雅各比系数）连接起来的身份。我们的论文是Gamboa，Nagel和Rouault（2016）的扩展，我们在其中仅使用概率工具（即大偏差理论）展示了总和规则。在这里，我们证明了在两种一般情况下单位不变随机矩阵的加权光谱度量的大偏差原理：首先，当平衡度量不一定由单个间隔支撑，其次，当电势是非阴性的多项式时。速率函数可以表示为Jacobi系数的函数。这些新的大偏差结果导致了One和Multi-Cut制度的原始总和规则，并回答了Gamboa，Nagel和Rouault（2016）关于一般总和规则的猜想。
A sum rule is an identity connecting the entropy of a measure with coefficients involved in the construction of its orthogonal polynomials (Jacobi coefficients). Our paper is an extension of Gamboa, Nagel and Rouault (2016), where we have showed sum rules by using only probabilistic tools (namely the large deviations theory). Here, we prove large deviation principles for the weighted spectral measure of unitarily invariant random matrices in two general situations: firstly, when the equilibrium measure is not necessarily supported by a single interval and secondly, when the potential is a nonnegative polynomial. The rate functions can be expressed as functions of the Jacobi coefficients. These new large deviation results lead to original sum rules both for the one and the multi-cut regime and also answer a conjecture stated in Gamboa, Nagel and Rouault (2016) concerning general sum rules.
