On the Correlation Functions of the Characteristic Polynomials of Real Random Matrices with Independent Entries

Автор(и)

  • Ievgenii Afanasiev B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine

DOI:

https://doi.org/10.15407/mag16.02.091

Ключові слова:

теорія випадкових матриць, ансамбль Жинібра, кореляційні функції характеристичних поліномів, моменти характеристичних поліномів, суперсиметрія

Анотація

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

Посилання

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Afanasiev, I. On the Correlation Functions of the Characteristic Polynomials of Real Random Matrices with Independent Entries. Журн. мат. фіз. анал. геом. 2020, 16, 91-118.

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