On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs
DOI:
https://doi.org/10.15407/mag13.03.268Анотація
Ми розглядаємо ансамбль дiйсних симетричних випадкових матриць H(n,ρ), отриманих з детермiнантної форми дзета-функцiї Iхари випадкових графiв, що мають n вершин з ймовiрнiстю ребра ρ/n. Ми доводимо, що нормована лiчильна функцiя власних значень H(n,ρ) слабко збiгається в середньому, коли n, ρ→∞ та ρ = o(nα), для кожного α > 0, до зсуву напiвкругового розподiлу Вiгнера. Нашi результати пiдтверджують припущення, що нескiнченнi випадковi графи Ердеша-Реньє задовольняють у середньому слабку версiю гiпотези Рiмана теорiї графiв.
Mathematics Subject Classification: 05C50, 05C80, 15B52, 60F99.
Ключові слова:
випадкові графи, випадкові матриці, дзета-функція Іхари, розподіл власних значеньПосилання
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