EMPIRICAL DISTRIBUTIONS OF LAPLACIAN MATRICES OF LARGE DILUTE RANDOM GRAPHS
2012 ◽
Vol 01
(03)
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pp. 1250004
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Keyword(s):
Large N
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We study the spectral properties of the Laplacian matrices and the normalized Laplacian matrices of the Erdös–Rényi random graph G(n, pn) for large n. Although the graph is simple, we discover some interesting behaviors of the two Laplacian matrices. In fact, under the dilute case, that is, pn ∈ (0, 1) and npn → ∞, we prove that the empirical distribution of the eigenvalues of the Laplacian matrix converges to a deterministic distribution, which is the free convolution of the semi-circle law and N(0, 1). However, for its normalized version, we prove that the empirical distribution converges to the semi-circle law.
2019 ◽
Vol 10
(01)
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pp. 2150009
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2018 ◽
Keyword(s):
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Keyword(s):
Keyword(s):
1975 ◽
Vol 77
(2)
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pp. 313-324
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Keyword(s):
2009 ◽
Vol 18
(4)
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pp. 583-599
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