Random incidence matrices: moments of the spectral density

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

39 pages, 9 figures, Latex2e, [v2: ref. added, Sect. 4 modified]

Scientific paper

We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the eigenvalue distribution as explicit polynomials in N and p. For large N and fixed p the spectrum contains a large eigenvalue at Np and a semi-circle of "small" eigenvalues. For large N and fixed average connectivity pN (dilute or sparse random matrices limit), we show that the spectrum always contains a discrete component. An anomaly in the spectrum near eigenvalue 0 for connectivity close to e=2.72... is observed. We develop recursion relations to compute the moments as explicit polynomials in pN. Their growth is slow enough so that they determine the spectrum. The extension of our methods to the Laplacian matrix is given in Appendix. Keywords: random graphs, random matrices, sparse matrices, incidence matrices spectrum, moments

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Random incidence matrices: moments of the spectral density does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random incidence matrices: moments of the spectral density, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random incidence matrices: moments of the spectral density will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-574774

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.