On the Correlation Functions of the Characteristic Polynomials of Real Random Matrices with Independent Entries
DOI:
https://doi.org/10.15407/mag16.02.091Анотація
У статті розглянуто кореляційні функції характеристичних поліномів дійсних випадкових матриць з незалежними елементами та встановлено асимптотичну поведінку цих кореляційних функцій у формі деякого інтеграла за інваріантною мірою по множині унітарних самодуальних матриць. Цей інтеграл обчислено для кореляційної функції другого порядку. З одержаної асимптотики випливає, що кореляційні функції ведуть себе таким же чином, як і у випадку дійсного ансамблю Жинібра з точністю до множника, що залежить лише від четвертого моменту спільного розподілу ймовірностей матричних елементів.Mathematics Subject Classification: 60B20, 15B52
Ключові слова:
теорія випадкових матриць, ансамбль Жинібра, кореляційні функції характеристичних поліномів, моменти характеристичних поліномів, суперсиметріяПосилання
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