Schur Function Expansion in Non-Hermitian Ensembles and Averages of Characteristic Polynomials

IF 1.4 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
Alexander Serebryakov, Nick Simm
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引用次数: 0

Abstract

We study k-point correlators of characteristic polynomials in non-Hermitian ensembles of random matrices, focusing on the Ginibre and truncated unitary random matrices. Our approach is based on the technique of character expansions, which expresses the correlator as a sum over partitions involving Schur functions. We show how to sum the expansions in terms of representations which interchange the role of k with the matrix size N. We also provide a probabilistic interpretation of the character expansion analogous to the Schur measure, linking the correlators to the distribution of the top row in certain Young diagrams. In more specific examples, we evaluate these expressions in terms of \(k \times k\) determinants or Pfaffians.

Abstract Image

非ermitian集合中的舒尔函数展开和特征多项式的平均值
我们研究了非赫米提随机矩阵集合中特征多项式的 k 点相关器,重点是 Ginibre 和截断单元随机矩阵。我们的方法基于特征展开技术,它将相关器表示为涉及舒尔函数的分区之和。我们还提供了与舒尔量度类似的特征展开的概率解释,将相关因子与某些杨图中顶行的分布联系起来。在更具体的例子中,我们用 \(k \times k\) 行列式或 Pfaffians 来评估这些表达式。
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来源期刊
Annales Henri Poincaré
Annales Henri Poincaré 物理-物理:粒子与场物理
CiteScore
3.00
自引率
6.70%
发文量
108
审稿时长
6-12 weeks
期刊介绍: The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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