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Exact equivalences and phase discrepancies between random matrix ensembles
Journal of Statistical Mechanics: Theory and Experiment ( IF 2.4 ) Pub Date : 2020-08-19 , DOI: 10.1088/1742-5468/aba594
Leonardo Santilli 1 , Miguel Tierz 1, 2
Affiliation  

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 $N$.

中文翻译:

随机矩阵系综之间的精确等价和相位差异

我们研究了在分区上考虑相同概率度量时出现的两种随机矩阵集合。一个是带有硬墙的 Meixner 系综,另一个是两个酉矩阵模型族,其权重函数可以解释为特征多项式插入。我们表明模型虽然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。根据模型,我们发现二阶和三阶相变。其他关系,通过直接映射,在酉矩阵模型和连续随机矩阵系综之间,Cauchy-Romanovski 类型,被精确地和渐近地呈现和研究。
更新日期:2020-08-19
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