Fetching the paper…
Reading the bibliography…
We consider the ensemble of adjacency matrices of Erd\H{o}s-R\'{e}nyi random graphs, that is, graphs on $N$ vertices where every edge is chosen independently and with probability $p\equiv p(N)$.
1955
Earlier work this paper cites.
Guionnet, AliceA. (2009). Large Random Matrices: Lectures on Macroscopic Asymptotics. Lecture Notes in Math. 1957. Springer, Berlin
1957
Earlier work this paper cites.
Erdős, P.P. andRényi, A.A. (1959). On random graphs. I. Publ. Math. Debrecen 6 290–297
1959
Earlier work this paper cites.
Erdős, P.P. andRényi, A.A. (1960). On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 17–61
1960
Earlier work this paper cites.
Gaudin, M.M. (1961). Sur la loi limite de l’espacement des valeurs propres d’une matrice aléatoire. Nuclear Phys. 25 447–458
1961
Earlier work this paper cites.
Dyson, Freeman J.F. J. (1962). A Brownian-motion model for the eigenvalues of a random matrix. J. Math. Phys. 3 1191–1198
1962
Earlier work this paper cites.
Mehta, Madan LalM. L. (1991). Random Matrices, 2nd ed. Academic Press, Boston, MA
1991
Earlier work this paper cites.
Sinaĭ, Ya. G.Y. G. andSoshnikov, A. B.A. B. (1998). A refinement of Wigner’s semicircle law in a neighborhood of the spectrum edge for random symmetric matrices. Funct. Anal. Appl. 32 114–131
1998
Earlier work this paper cites.
Bleher, PavelP. andIts, AlexanderA. (1999). Semiclassical asymptotics of orthogonal polynomials, Riemann–Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 185–266
1999
Earlier work this paper cites.
Deift, P.P., Kriecherbauer, T.T., McLaughlin, K. T. R.K. T. R., Venakides, S.S. andZhou, X.X. (1999). Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 52 1335–1425
1999
Earlier work this paper cites.
Deift, P.P., Kriecherbauer, T.T., McLaughlin, K. T-RK. T.-R., Venakides, S.S. andZhou, X.X. (1999). Strong asymptotics of orthogonal polynomials with respect to exponential weights. Comm. Pure Appl. Math. 52 1491–1552
1999
Earlier work this paper cites.
Deift, P. A.P. A. (1999). Orthogonal Polynomials and Random Matrices: A Riemann–Hilbert Approach. Courant Lecture Notes in Mathematics 3. Amer. Math Soc., Providence, RI
1999
Earlier work this paper cites.
Soshnikov, AlexanderA. (1999). Universality at the edge of the spectrum in Wigner random matrices. Comm. Math. Phys. 207 697–733
1999
Earlier work this paper cites.
Guionnet, A.A. andZeitouni, O.O. (2000). Concentration of the spectral measure for large matrices. Electron. Commun. Probab. 5 119–136 (electronic)
2000
Earlier work this paper cites.
Bai, Z. D.Z. D., Miao, BaiqiB. andTsay, JhishenJ. (2002). Convergence rates of the spectral distributions of large Wigner matrices. Int. Math. J. 1 65–90
2002
Cited alongside, same era.
Féral, DelphineD. andPéché, SandrineS. (2007). The largest eigenvalue of rank one deformation of large Wigner matrices. Comm. Math. Phys. 272 185–228
2007
Cited alongside, same era.
Vu, Van H.V. H. (2007). Spectral norm of random matrices. Combinatorica 27 721–736
2007
Cited alongside, same era.
Pastur, L.L. andShcherbina, M.M. (2008). Bulk universality and related properties of Hermitian matrix models. J. Stat. Phys. 130 205–250
2008
Cited alongside, same era.
Capitaine, MireilleM., Donati-Martin, CatherineC. andFéral, DelphineD. (2009). The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations. Ann. Probab. 37 1–47
Tao, TerenceT. andVu, VanV. (2010). Random matrices: Universality of local eigenvalue statistics up to the edge. Comm. Math. Phys. 298 549–572
2010
Later among the works it cites.
Tran, L.L., Vu, V.V. andWang, K.K. (2010). Sparse random graphs: Eigenvalues and eigenvectors. Preprint. Available at arXiv: \arxivurl
2010
Later among the works it cites.
Benaych-Georges, FlorentF. andNadakuditi, Raj RaoR. R. (2011). The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Adv. Math. 227 494–521
2011
Closest in time.
Dekel, Y.Y., Lee, R. L.R. L. andLinial, N.N. (2011). Eigenvectors of random graphs: Nodal domains. Random Structures Algorithms 39 39–58
2011
Closest in time.
Dumitriu, I.I. andPal, S.S. (2011). Sparse regular random graphs: Spectral density and eigenvectors. Preprint. Available at arXiv: \arxivurl
2011
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2009
Cited alongside, same era.
Deift, PercyP. andGioev, DimitriD. (2009). Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes in Mathematics 18. Amer. Math. Soc., Providence, RI
2009
Cited alongside, same era.
Erdős, LászlóL., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2009). Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. Ann. Probab. 37 815–852
2009
Cited alongside, same era.
Erdős, LászlóL., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2009). Local semicircle law and complete delocalization for Wigner random matrices. Comm. Math. Phys. 287 641–655
2009
Cited alongside, same era.
Anderson, Greg W.G. W., Guionnet, AliceA. andZeitouni, OferO. (2010). An Introduction to Random Matrices. Cambridge Studies in Advanced Mathematics 118. Cambridge Univ. Press, Cambridge
2010
Cited alongside, same era.
Erdős, LászlóL., Péché, SandrineS., Ramírez, José A.J. A., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2010). Bulk universality for Wigner matrices. Comm. Pure Appl. Math. 63 895–925
2010
Cited alongside, same era.
Erdős, LászlóL., Ramírez, José A.J. A., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2010). Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation. Electron. J. Probab. 15 526–603
2010
Cited alongside, same era.
Erdős, LászlóL., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2010). Wegner estimate and level repulsion for Wigner random matrices. Int. Math. Res. Not. IMRN 3 436–479
2010
Cited alongside, same era.
Closest in time.
Erdős, LászlóL., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2011). Universality of random matrices and local relaxation flow. Invent. Math. 185 75–119
2011
Closest in time.
Erdős, LászlóL., Yau, Horng-TzerH.-T. andYin, JunJ. (2011). Universality for generalized Wigner matrices with Bernoulli distribution. J. Comb. 2 15–81
2011
Closest in time.
Tao, TerenceT. andVu, VanV. (2011). Random matrices: Universality of local eigenvalue statistics. Acta Math. 206 127–204
2011
Closest in time.
Erdős, L.L., Knowles, A.A., Yau, H. T.H. T. andYin, J.J. (2012). Spectral statistics of Erdős–Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Comm. Math. Phys. 314 587–640
2012
Closest in time.
Erdős, L.L., Schlein, B.B., Yau, H. T.H. T. andYin, J.J. (2012). The local relaxation flow approach to universality of the local statistics for random matrices. Ann. Inst. H. Poincaré Probab. Statist. 48 1–46
2012
Closest in time.
Erdős, L.L., Yau, H. T.H. T. andYin, J.J. (2012). Bulk universality for generalized Wigner matrices. Probab. Theory Related Fields 154 341–407
2012
Closest in time.
Erdős, LászlóL., Yau, Horng-TzerH.-T. andYin, JunJ. (2012). Rigidity of eigenvalues of generalized Wigner matrices. Adv. Math. 229 1435–1515
2012
Closest in time.
Pizzo, A.A., Renfrew, D.D. andSoshnikov, A.A. (2013). On finite rank deformations of Wigner matrices. Ann. Inst. Henri Poincaré Probab. Stat. 49 64–94
2013
Closest in time.