论文标题
随机矩阵合奏之间的确切等价和相位差异
Exact equivalences and phase discrepancies between random matrix ensembles
论文作者
论文摘要
我们研究了两种类型的随机矩阵集合，它们在考虑分区的相同概率度量时会出现。一个是带有硬墙的梅克斯纳集团，另一个是两个单位矩阵模型的家族，重量函数可以解释为特征多项式插入。我们表明，模型对参数的固定值具有相同的精确评估，但可能会呈现不同的相结构。我们发现第二和三阶的相变，具体取决于模型。通过直接映射，在统一矩阵模型和实际线上连续的随机矩阵合奏之间的其他关系（Cauchy-Romanovski型）的连续矩阵集合被确切地呈现和研究。还研究了正交和符号群体的案例，并与Chebyshev多项式的Wronskians有关，我们大致评估了$ n $。
We study two types of random matrix ensembles that emerge when considering the same probability measure on partitions. One is the Meixner ensemble with a hard wall and the other are two families of unitary matrix models, with weight functions that can be interpreted as characteristic polynomial insertions. We show that the models, while having the same exact evaluation for fixed values of the parameter, may present a different phase structure. We find phase transitions of the second and third order, depending on the model. Other relationships, via direct mapping, between the unitary matrix models and continuous random matrix ensembles on the real line, of Cauchy-Romanovski type, are presented and studied both exactly and asymptotically. The case of orthogonal and symplectic groups is studied as well and related to Wronskians of Chebyshev polynomials, that we evaluate at large $N$.
