On the Correlation Functions of the Characteristic Polynomials of Random Matrices with Independent Entries: Interpolation Between Complex and Real Cases
DOI:
https://doi.org/10.15407/mag18.02.159Анотація
У роботi розглянуто кореляцiйнi функцiї характеристичних полiномiв випадкових матриць з незалежними комплексними елементами. Ми дослiдили те, як асимптотична поведiнка кореляцiйних функцiй залежить вiд другого моменту спiльного закону розподiлу ймовiрностей для матричних елементiв, при цьому другий момент можна трактувати як свого роду “мiру дiйсностi” елементiв. Показано, що кореляцiйнi функцiї ведуть себе таким же чином, як i у випадку комплексного ансамблю Жинiбра, з точнiстю до множника, що залежить лише вiд другого моменту та абсолютного четвертого моменту спiльного розподiлу ймовiрностей матричних елементiв.
Mathematical Subject Classification 2010: 60B20, 15B52
Ключові слова:
теорiя випадкових матриць, ансамбль Жинiбра, кореляцiйнi функцiї характеристичних полiномiв, моменти характеристичних полiномiв, суперсиметрiяПосилання
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