The spectrum of a random geometric graph is concentrated

Journal of Theoretical Probability

Volumn 20, Issue 2, 2007, Pages 119-132

  Rai, Sanatan ^a  

^a Stanford University   (United States)

Author keywords

Random geometric graphs; Spectral measure

Indexed keywords

EID: 34249067134     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-006-0049-7     Document Type: Article

References (17)

1. Bai, Z. D. (1993). Convergence rate of expected spectral distributions of large random matrices, part i: Wigner matrices, part ii: sample covariance matrices. Ann. Probab.
2. Booth, L., Bruck, J., Franceschetti, M., and Meester, R. (2003). Covering algorithms, continuum percolation and the geometry of wireless networks. Ann. Appl. Probab. 13(2), 722-741.
3. Boyd, S., Ghosh, A., Prabhakar, B., and Shah, D. (2004). Mixing times of random walk on geometric random graphs. Submitted for publication.
4. Goel, A., Rai, S., and Krishnamachari, B. (2004). Sharp thresholds for monotone properties in random geometric graphs. In Proceedings of the Symposium on the Theory of Computing, pages 13-23.
5. Gray, R. M. (1971). Toeplitz and circulant matrices: A review. Revised 2002, URL: http://ee.stanford.edu/gray/toplitz.pdf.
6. Guionnet, A., and Zeituni, O. (2000). Concentration of the spectral measure for large matrices. Electron. Commun. Probab. 9, 119-236.
7. Gupta, P., and Kumar, P. R. (1998). Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, chapter Critical power for asymptotic connectivity in wireless networks. Birkhauser, Boston.
8. Janson, S., and Luczak, T., Ruciński, A. (2000). Random Graphs, Wiley Interscience series in discrete mathematics and optimization. Wiley-Interscience, New York.
9. Koltchinskii, V.I. (1998). Asymptotics of spectral projections of some random matrices approximating integral operators. In Eberlein, E., Hahn, M., Talagrand, M. (eds.). High Dimensional Probability, volume 43 of Progress in Probability, Birkhauser, pages 191-227.
10. Koltchinskii, V.I., Giné, E. (2000). Random matrix approximation of spectra of integral operator. Bernoulli.
11. d with ergodic random bond conductivities. Commun. Math. Phys. 90, 27-68.
12. Leighton, F.T., Shor, P.W. (1989). Tight bounds for minimax grid matching, with applications to the average case analysis of algorithms. Combinatorica 9, 161-187.
13. Penrose, M.D. (2003). Random Geometric Graphs, Volume 5 of Oxford Studies in Probability, Oxford University Press, oxford.
14. Pólya, G., Szëgo, G. (1998). Problems and Theorems in Analysis I. Springer-Verlag, Berlin (reprint edition).
15. Shor, P.W., Yukich, J.E. (1991). Minmax grid matching and empirical measures. Ann. Probab. 19(3), 1338-1348.
16. Trench, W.F. (2003). Absolute equal distribution of the spectra of hermitian matrices. Linear Algebra and Its Applications.
17. Wigner, E.P. (1985). On the distribution of the roots of certain symmetric matrices. Ann. Math. 67, 325-327.