Advanced search
Publication Cover
Experimental Mathematics Volume 17, 2008 - Issue 2
Submit an article Journal homepage
63
Views
28
CrossRef citations to date
0
Altmetric
Original Article

The Distribution of the Largest Nontrivial Eigenvalues in Families of Random Regular Graphs

Steven J. Miller Department of Mathematics, Williams College, Williamstown, MA 01267
,
Tim Novikoff Center for Applied Mathematics, Cornell University, 657 Frank Rhodes Hall, Ithaca, NY 14853
&
Anthony Sabelli Center for Applied Mathematics, Cornell University, 657 Frank Rhodes Hall, Ithaca, NY 14853
Pages 231-244 | Published online: 30 Jan 2011

Citations (28)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (1)

Igor Rivin & Naser T. Sardari. (2019) Quantum Chaos on Random Cayley Graphs of . Experimental Mathematics 28:3, pages 328-341.
Read now

Articles from other publishers (27)

Hamid Asadi & Babak Seyfe. (2023) Model order estimation based on the correntropy of observation eigenvalues. Signal Processing, pages 109310.
Crossref
Roger Van Peski. (2019) Spectral distributions of periodic random matrix ensembles. Random Matrices: Theory and Applications 10:01, pages 2150011.
Crossref
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles & Horng-Tzer Yau. (2020) Edge rigidity and universality of random regular graphs of intermediate degree. Geometric and Functional Analysis 30:3, pages 693-769.
Crossref
Roland Bauerschmidt, Jiaoyang Huang & Horng-Tzer Yau. (2019) Local Kesten–McKay Law for Random Regular Graphs. Communications in Mathematical Physics 369:2, pages 523-636.
Crossref
Ryan C. Chen, Yujin H. Kim, Jared D. Lichtman, Steven J. Miller, Shannon Sweitzer & Eric Winsor. (2019) Spectral statistics of non-Hermitian random matrix ensembles. Random Matrices: Theory and Applications 08:02, pages 1950005.
Crossref
O. Khorunzhiy. (2018) Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs. Random Matrices: Theory and Applications 07:03, pages 1850007.
Crossref
Paula Burkhardt, Peter Cohen, Jonathan DeWitt, Max Hlavacek, Steven J. Miller, Carsten Sprunger, Yen Nhi Truong Vu, Roger Van Peski & Kevin Yang. (2018) Random matrix ensembles with split limiting behavior. Random Matrices: Theory and Applications 07:03, pages 1850006.
Crossref
Nicholas Cook, Larry Goldstein & Tobias Johnson. (2018) Size biased couplings and the spectral gap for random regular graphs. The Annals of Probability 46:1.
Crossref
Chris Hall, Doron Puder & William F. Sawin. (2018) Ramanujan coverings of graphs. Advances in Mathematics 323, pages 367-410.
Crossref
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles & Horng-Tzer Yau. (2017) Bulk eigenvalue statistics for random regular graphs. The Annals of Probability 45:6A.
Crossref
Roland Bauerschmidt, Antti Knowles & Horng-Tzer Yau. (2017) Local Semicircle Law for Random Regular Graphs. Communications on Pure and Applied Mathematics 70:10, pages 1898-1960.
Crossref
Chris Hall, Doron Puder & William F. Sawin. (2016) Ramanujan coverings of graphs. Ramanujan coverings of graphs.
Corey Manack & Steven J. Miller. (2015) Leading digit laws on linear Lie groups. Research in Number Theory 1:1.
Crossref
Doron Puder. (2014) Expansion of random graphs: new proofs, new results. Inventiones mathematicae 201:3, pages 845-908.
Crossref
Christopher H Joyner & Uzy Smilansky. (2015) Spectral statistics of Bernoulli matrix ensembles—a random walk approach (I). Journal of Physics A: Mathematical and Theoretical 48:25, pages 255101.
Crossref
Steven J. Miller, Kirk Swanson, Kimsy Tor & Karl Winsor. (2015) Limiting spectral measures for random matrix ensembles with a polynomial link function. Random Matrices: Theory and Applications 04:02, pages 1550004.
Crossref
Leo Goldmakher, Cap Khoury, Steven J. Miller & Kesinee Ninsuwan. (2014) On the spectral distribution of large weighted random regular graphs. Random Matrices: Theory and Applications 03:04, pages 1450015.
Crossref
Tobias Johnson & Soumik Pal. (2014) Cycles and eigenvalues of sequentially growing random regular graphs. The Annals of Probability 42:4.
Crossref
Mike Krebs & Anthony Shaheen. 2013. Handbook of Graph Theory, Second Edition. Handbook of Graph Theory, Second Edition 1337 1347 .
Murat Koloğlu, Gene S. Kopp & Steven J. Miller. (2011) The Limiting Spectral Measure for Ensembles of Symmetric Block Circulant Matrices. Journal of Theoretical Probability 26:4, pages 1020-1060.
Crossref
László Erdős, Antti Knowles, Horng-Tzer Yau & Jun Yin. (2012) Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues. Communications in Mathematical Physics 314:3, pages 587-640.
Crossref
Yoshiyuki Kabashima & Hisanao Takahashi. (2012) First eigenvalue/eigenvector in sparse random symmetric matrices: influences of degree fluctuation. Journal of Physics A: Mathematical and Theoretical 45:32, pages 325001.
Crossref
Eyal Lubetzky, Benny Sudakov & Van Vu. (2011) Spectra of lifted Ramanujan graphs. Advances in Mathematics 227:4, pages 1612-1645.
Crossref
Nen Saito & Yukito Iba. (2011) Probability of graphs with large spectral gap by multicanonical Monte Carlo. Computer Physics Communications 182:1, pages 223-225.
Crossref
Frank Firk & Steven Miller. (2009) Nuclei, Primes and the Random Matrix Connection. Symmetry 1:1, pages 64-105.
Crossref
Sasha Sodin. (2009) The Tracy–Widom Law for Some Sparse Random Matrices. Journal of Statistical Physics 136:5, pages 834-841.
Crossref
Guilhem Semerjian, Marco Tarzia & Francesco Zamponi. (2009) Exact solution of the Bose-Hubbard model on the Bethe lattice. Physical Review B 80:1.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.