First eigenvalue/eigenvector in sparse random symmetric matrices: influences of degree fluctuation
نویسندگان
چکیده
منابع مشابه
Gaussian fluctuation in random matrices.
Let N(L) be the number of eigenvalues, in an interval of length L, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of N by N matrices, in the limit N → ∞. We prove that [N(L) − 〈N(L)〉]/√logL has a Gaussian distribution when L → ∞. This theorem, which requires control of all the higher moments of the distribution, elucidates numerical and exact results ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2012
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/45/32/325001