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A connection between the bipartite complements of line graphs and the line graphs with two positive eigenvalues
line graphs graph spectra complements Courant-Weyl inequalities
2012/4/16
In 1974 Cvetkovi\'c and Simi\'c showed which graphs $G$ are the bipartite complements of line graphs. In 2002 Borovi\'canin showed which line graphs $L(H)$ have third largest eigenvalue $\lambda_3\leq...
How many eigenvalues of a Gaussian random matrix are positive?
Gaussian random matrices large deviations Coulomb gas method index
2011/3/2
We study the probability distribution of the index N+, i.e., the number of positive eigenvalues of an N × N Gaussian random matrix. We show analytically that, for large N and large N+ with the fractio...