Повнотекстовий пошук
Пошуковий запит: (<.>AT=Khorunzhiy On Eigenvalue Distribution of$<.>) |
Загальна кількість знайдених документів : 1
|
1. |
Khorunzhiy O. On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs [Електронний ресурс] / O. Khorunzhiy // Журнал математической физики, анализа, геометрии. - 2017. - Т. 13, № 3. - С. 268-282. - Режим доступу: http://nbuv.gov.ua/UJRN/jmfag_2017_13_3_6 We consider the ensemble of real symmetric random matrices <$EH sup {(n, rho )}> obtained from the determinant form of the Ihara zeta function of random graphs that have n vertices with the edge probability <$Erho "/" n>. We prove that the normalized eigenvalue counting function of <$EH sup {(n, rho )}> converges weakly in average as <$En,~rho~symbol О~inf> and <$Erho~=~o(n sup alpha )> for any <$Ealpha~>>~0> to a shift of the Wigner semi-circle distribution. Our results support a conjecture that the large Erdos - Renyi random graphs satisfy in average the weak graph theory Riemann Hypothesis.
|
|
|