多奇电荷对数气体的配分函数

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2021-05-29 DOI:10.1142/S2010326322500411

Elisha D. Wolff, John Wells

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引用次数: 1

摘要

我们使用洗牌代数中的技术，以相关非齐次交替张量的Berezin积分的形式，给出了在一定逆温度β下由(可能)不同整数电荷的粒子组成的一维对数气体的配分函数公式。这通过消除对奇电荷种类数的限制推广了先前已知的结果。我们的方法提供了一个统一的框架，将de Bruijn积分恒等式从经典的β系综(β = 1,2,4)扩展到多组分系综，以及更一般的行列式积分的迭代积分。

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The Partition Function of Log-Gases with Multiple Odd Charges

We use techniques in the shuﬄe algebra to present a formula for the partition function of a one-dimensional log-gas comprised of particles of (possibly) diﬀerent integer charges at certain inverse temperature β in terms of the Berezin integral of an associated non-homogeneous alternating tensor. This generalizes previously known results by removing the restriction on the number of species of odd charge. Our methods provide a uniﬁed framework extending the de Bruijn integral identities from classical β ensembles ( β = 1 , 2 , 4) to multicomponent ensembles, as well as to iterated integrals of more general determinantal integrands.

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.