Loose laplacian spectra of random hypergraphs

Random Structures and Algorithms

Volumn 41, Issue 4, 2012, Pages 521-545

  Lu, Linyuan ^a   Peng, Xing ^a  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Loose Laplacians of hypergraphs; Random hypergraphs; Semi circle Law

Indexed keywords

EID: 84868301297     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20443     Document Type: Article

References (34)

1. R. Ahlswede and A. Winter, Strong converse for identification via quantum channels, IEEE Trans Inform Theory 48 ( 2002), 569-579.
2. N. Alon, M. Krivelevich, and V. H. Vu, Concentration of eigenvalues of random matrices, Israel Math J 131 ( 2002), 259-267.
3. A. R. Calderbank and P. Frankl, Improved upper bounds concerning the Erdos-Ko-Rado Theorem, Combin, Probab Comput 1 ( 1992), 115-122.
4. H. Chernoff, A note on an inequality involving the normal distribution, Ann Probab 9 ( 1981), 533-535.
5. F. Chung, Diameters and eigenvalues, J Am Math Soc 2 ( 1989), 187-196.
6. F. Chung, The Laplacian of a hypergraph, Expanding graphs (DIMACS series), In J. Friedman (Editor), Am. Math. Soc., Providence, RI, 1993, pp. 21-36.
7. F. Chung, V. Faber, and T. A. Manteuffel, An upper bound on the diameter of a graph from eigenvalues associated with its Laplacian, Siam J Disc Math 7 ( 1994), 443-457.
8. F. Chung, Spectral graph theory, CBMS Regional Conference Series in Mathematics, Vol. 92, Conference Board of the Mathematical Sciences, Washington, DC, 1997.
9. F. Chung, Laplacians and the Cheeger inequality for directed graphs, Ann Combin 9 ( 2005), 1-19.
10. F. Chung, The diameter and Laplacian eigenvalues of directed graphs, Electron J Combin 13 ( 2006), N4.
11. F. Chung, L. Lu, and V. H. Vu, Eigenvalues of random power law graphs, Ann Combin 7 ( 2003), 21-33.
12. F. Chung, L. Lu, and V. H. Vu, Spectra of random graphs with given expected degrees, Proc Nat Acad Sci 100 ( 2003), 6313-6318.
13. F. Chung and M. Radcliffe, On the spectra of general random graphs, Electron J Combin 18 ( 2011), p. 215.
14. A. Coja-Oghlan, On the Laplacian eigenvalues of G(n, p), Combin, Probab Comput 16 ( 2007), 923-946.
15. A. Coja-Oghlan and A. Lanka, The spectral gap of random graphs with given expected degrees, Electron J Combin 16 ( 2009), R138.
16. D. Cristofides, and K. Markström, Expansion properties of random Cayley graphs and vertex transitive graphs via matrix martingales, Random Struct Algorithms 32 ( 2008), 88-100.
17. X. Ding and T. Jiang, Spectral distributions of adjacency and Laplacian matrices of random graphs, Ann Appl Probab 20 ( 2010), 2086-2117.
18. P. Erdos, C. Ko, and R. Rado, Intersection theorems for systems of finite sets, Quarter J Math, Oxford Series, series 2 ( 1961), 313-320.
19. U. Feige and E. Ofek, Spectral techniques applied to sparse random graphs, Random Struct Algorithms 27 ( 2005), 251-275.
20. J. Friedman, J. Kahn, and E. Szemerédi, On the second eigenvalue in random regular graphs, In Proc. 21st ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1989, pp. 587-598.
21. J. Friedman, On the second eigenvalue and random walks in randomd-regular graphs, Combinatorica 11 ( 1991), 331-362.
22. J. Friedman, A Proof of Alon's second eigenvalue conjectureand related problem, Memoirs of the American Mathematical Society, 2008, p. 100.
23. Z. Füredi and J. Komlós, The eigenvalues of random symmetric matrices, Combinatorica 1 ( 1981), 233-241.
24. C. Godsil and G. Royle, Algebraic graph theory, Springer-Verlag, New York, 2001.
25. D. Gross, Recovering low-rank matrices from few coefficients in any basis, IEEE Trans Inform Theory 57 ( 2011), 1548-1566.
26. S.-G. Hwang, Cauchy's interlace theorem for eigenvalues of Hermitian matrices, Amer Math Monthly 111 ( 2004), 157-159.
27. G. O. H. Katona, A simple proof of the Erdos-Chao Ko-Rado theorem, J Combin Theory, Series B 13 ( 1972), 183-184.
28. M. Krivelevich and B. Sudakov, The largest eigenvalue of sparse random graphs, Combin, Probab Comput 12 ( 2003), 61-72.
29. L. Lu, and X. Peng, High-ordered random walks and generalized Laplacians on hypergraphs, In A. Frieze, P. Horn, P. Pralat (Editors), Algorithms and Models for the Web Graph-8th International Workshop, (WAW 2011) Proceedings, Lecture Notes in Computer Science, 6732, Springer, 2011, pp. 14-25.
30. R. Oliveira, Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges, Submitted for publication. http://arxiv.org/abs/0911.0600.
31. B. Recht, Simpler approach to matrix completion, J Mach Learn Res 12 ( 2011), 3413-3430.
32. J. Tropp, User-Friendly Tail Bounds for Sums of Random Matrices. Submitted for publication, doi:10.1007/s10208-011-9099-z, 2011.
33. J. A. Rodríguez, On the Laplacian spectrum and walk-regular hypergraphs, Linear Multilinear Algebra 51 ( 2003), 285-297.
34. J. A. Rodríguez, Laplacian eigenvalues and partition problems in hypergraphs, Appl Math Lett 22 ( 2009), 916-921.