论文标题
通过球形积分的大偏差原理
Large Deviation Principles via Spherical Integrals
论文作者
论文摘要
在本文中，我们开发了一个框架，通过使用[46,47]中获得的球形积分的限制来研究矩阵模型及其量化版本的大偏差原理及其量化版本。作为示例，我们获得了 1。对于$ ub_nu^*$的对角线条目的经验分布的大偏差原则，对于$ n \ times n $ n $对角矩阵$ b_n $和unity haar分布式矩阵$ u $; 2。用于$ a_n+ub_nu^*$的经验特征值分布的大偏差上限，对于$ n \ times n $ n $对角线矩阵$ a_n，b_n $的两个序列，及其互补的下限，并在衡量产品中描述的量度均描述了与融合的产品所描述的； 3。kostka编号的一个大偏差原理$ k _ {\boldsymbolλ_n\boldsymbolη_n} $，对于两个分区的两个序列$ \boldsymbolλ_n，\boldsymbolη_n$，最多最多$ n $ lows; 4。较大的偏差上限，用于利特伍德 - 里查森系数$ c _ {\boldsymbolλ_n\ boldsymbolη_n}^{\boldsymbolκ_n} $，分区的三个序列$ \boldsymbolλ_n，\boldsymbolλ_n，\ boldsymbol h $ n，互补的下限以不错的措施。
In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained in [46,47]. As examples, we obtain 1. a large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary Haar distributed matrices $U$; 2. a large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at measures which are described by the free product with amalgamation; 3. a large deviation principle for the Kostka number $K_{\boldsymbolλ_N \boldsymbolη_N}$, for two sequences of partitions $\boldsymbolλ_N, \boldsymbolη_N$ with at most $N$ rows; 4. a large deviation upper bound for the Littlewood-Richardson coefficients $c_{\boldsymbolλ_N \boldsymbol η_N}^{\boldsymbol κ_N}$, for three sequences of partitions $\boldsymbolλ_N, \boldsymbol η_N, \boldsymbol κ_N$ with at most $N$ rows, and their complementary lower bounds at nice measures.
