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Funktsional. Anal. i Prilozhen., 1998, Volume 32, Issue 2, Pages 56–79 (Mi faa411)  

This article is cited in 51 scientific papers (total in 51 papers)

A Refinement of Wigner's Semicircle Law in a Neighborhood of the Spectrum Edge for Random Symmetric Matrices

Ya. G. Sinaia, A. B. Soshnikovb

a Princeton University, Department of Mathematics
b Institute for Advanced Study, School of Mathematics

DOI: https://doi.org/10.4213/faa411

Full text: PDF file (1931 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 1998, 32:2, 114–131

Bibliographic databases:

UDC: 519.2
Received: 05.09.1997

Citation: Ya. G. Sinai, A. B. Soshnikov, “A Refinement of Wigner's Semicircle Law in a Neighborhood of the Spectrum Edge for Random Symmetric Matrices”, Funktsional. Anal. i Prilozhen., 32:2 (1998), 56–79; Funct. Anal. Appl., 32:2 (1998), 114–131

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Peche, S, “On the lower bound of the spectral norm of symmetric random matrices with independent entries”
    2. Peche S., Soshnikov A., “On the lower bound of the spectral norm of symmetric random matrices with independent entries”  mathscinet  isi
    3. Soshnikov, A, “Universality at the edge of the spectrum in Wigner random matrices”, Communications in Mathematical Physics, 207:3 (1999), 697  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Soshnikov, A, “The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities”, Annals of Probability, 28:3 (2000), 1353  crossref  mathscinet  zmath  isi
    5. Okounkov, A, “Random matrices and random permutations”, International Mathematics Research Notices, 2000, no. 20, 1043  crossref  mathscinet  zmath  isi
    6. Soshnikov, AB, “Gaussian fluctuation for the number of particles in Airy, Bessel, Sine, and other determinantal random point fields”, Journal of Statistical Physics, 100:3–4 (2000), 491  crossref  mathscinet  zmath  isi
    7. Khorunzhy, A, “Sparse random matrices: Spectral edge and statistics of rooted trees”, Advances in Applied Probability, 33:1 (2001), 124  crossref  mathscinet  zmath  isi  scopus
    8. Johansson, K, “Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices”, Communications in Mathematical Physics, 215:3 (2001), 683  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Soshnikov, A, “A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices”, Journal of Statistical Physics, 108:5–6 (2002), 1033  crossref  mathscinet  zmath  isi  scopus
    10. Cicuta, GM, “Enumeration of simple random walks and tridiagonal matrices”, Journal of Physics A-Mathematical and General, 35:5 (2002), 1125  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Gamburd A., “Expander graphs, random matrices and quantum chaos”, Random Walks and Geometry, 2004, 109–140  mathscinet  zmath  isi
    12. Soshnikov, A, “On the largest singular values of random matrices with independent Cauchy entries”, Journal of Mathematical Physics, 46:3 (2005), 033302  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Gamburd, A, “Poisson-Dirichlet distribution for random Belyi surfaces”, Annals of Probability, 34:5 (2006), 1827  crossref  mathscinet  zmath  isi  scopus
    14. Dumitriu, I, “Global spectrum fluctuations for the beta-Hermite and beta-Laguerre ensembles via matrix models”, Journal of Mathematical Physics, 47:6 (2006), 063302  crossref  mathscinet  zmath  adsnasa  isi  scopus
    15. Ruzmaikina, A, “Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries”, Communications in Mathematical Physics, 261:2 (2006), 277  crossref  mathscinet  zmath  adsnasa  isi  scopus
    16. Peche, S, “Wigner random matrices with non-symmetrically distributed entries”, Journal of Statistical Physics, 129:5–6 (2007), 857  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. Feral, D, “The largest eigenvalue of rank one deformation of large Wigner matrices”, Communications in Mathematical Physics, 272:1 (2007), 185  crossref  mathscinet  zmath  adsnasa  isi  scopus
    18. Volchenkov, D, “Markov chain methods for analyzing urban networks”, Journal of Statistical Physics, 132:6 (2008), 1051  crossref  mathscinet  zmath  adsnasa  isi  scopus
    19. Lytova, A, “CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES”, Annals of Probability, 37:5 (2009), 1778  crossref  mathscinet  zmath  isi  scopus
    20. Khorunzhiy, O, “UNIFORM BOUNDS FOR EXPONENTIAL MOMENT OF MAXIMUM OF A DYCK PATH”, Electronic Communications in Probability, 14 (2009), 327  crossref  mathscinet  zmath  isi  scopus
    21. Feral, D, “The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case”, Journal of Mathematical Physics, 50:7 (2009), 073302  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. Peche, S, “Universality results for the largest eigenvalues of some sample covariance matrix ensembles”, Probability Theory and Related Fields, 143:3–4 (2009), 481  crossref  mathscinet  zmath  isi  scopus
    23. Chatterjee, S, “Fluctuations of eigenvalues and second order Poincaré inequalities”, Probability Theory and Related Fields, 143:1–2 (2009), 1  crossref  mathscinet  zmath  isi  scopus
    24. Blanchard Ph., Dawin J.R., Volchenkov D., “Markov chains or the game of structure and chance”, The European Physical Journal Special Topics, 184:1 (2010), 1–82  crossref  adsnasa  isi  elib  scopus
    25. Tao T., Vu V., “Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge”, Comm Math Phys, 298:2 (2010), 549–572  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    26. Erdos L., “Universality of Wigner Random Matrices”, Xvith International Congress on Mathematical Physics, 2010, 86–105  crossref  mathscinet  zmath  isi  scopus
    27. L. Erdős, “Universality of Wigner random matrices: a survey of recent results”, Russian Math. Surveys, 66:3 (2011), 507–626  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    28. Tao T., Vu V., “The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices”, Electron J Probab, 16 (2011), 2104–2121  crossref  mathscinet  zmath  isi  scopus
    29. Erdos L., Schlein B., Yau H.-T., “Universality of random matrices and local relaxation flow”, Invent Math, 185:1 (2011), 75–119  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    30. Feray V., Sniady P., “Asymptotics of characters of symmetric groups related to Stanley character formula”, Ann of Math (2), 173:2 (2011), 887–906  crossref  mathscinet  zmath  isi  scopus
    31. Erdos L., Schlein B., Yau H.-T., Yin J., “The local relaxation flow approach to universality of the local statistics for random matrices”, Ann Inst Henri Poincaré Probab Stat, 48:1 (2012), 1–46  crossref  mathscinet  zmath  adsnasa  isi  scopus
    32. Erdos L., Yau H.-T., Yin J., “Rigidity of eigenvalues of generalized Wigner matrices”, Adv Math, 229:3 (2012), 1435–1515  crossref  mathscinet  zmath  isi  scopus
    33. Erdos L., Knowles A., Yau H.-T., Yin J., “Spectral Statistics of Erdas-R,Nyi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues”, Commun. Math. Phys., 314:3 (2012), 587–640  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    35. Zheng Sh., “Central Limit Theorems for Linear Spectral Statistics of Large Dimensional F-Matrices”, Ann. Inst. Henri Poincare-Probab. Stat., 48:2 (2012), 444–476  crossref  mathscinet  zmath  adsnasa  isi  scopus
    36. Wong P., “Local Semicircle Law at the Spectral Edge for Gaussian Beta-Ensembles”, Commun. Math. Phys., 312:1 (2012), 251–263  crossref  mathscinet  zmath  adsnasa  isi  scopus
    37. Sosoe Ph., Wong P., “Regularity Conditions in the Clt for Linear Eigenvalue Statistics of Wigner Matrices”, Adv. Math., 249 (2013), 37–87  crossref  mathscinet  zmath  isi  scopus
    38. Erdos L., Knowles A., Yau H.-T., Yin J., “Spectral Statistics of Erdos-Renyi Graphs I: Local Semicircle Law”, Ann. Probab., 41:3B (2013), 2279–2375  crossref  mathscinet  zmath  isi  scopus
    39. Knowles A., Yin J., “Eigenvector Distribution of Wigner Matrices”, Probab. Theory Relat. Field, 155:3-4 (2013), 543–582  crossref  mathscinet  zmath  isi  scopus
    40. O. Khorunzhiy, “On High Moments and the Spectral Norm of Large Dilute Wigner Random Matrices”, Zhurn. matem. fiz., anal., geom., 10:1 (2014), 64–125  mathnet  crossref  mathscinet
    41. Benaych-Georges F., Peche S., “Localization and Delocalization For Heavy Tailed Band Matrices”, Ann. Inst. Henri Poincare-Probab. Stat., 50:4 (2014), 1385–1403  crossref  mathscinet  zmath  isi  scopus
    42. Lee J.O., Schnelli K., “Edge Universality For Deformed Wigner Matrices”, Rev. Math. Phys., 27:8 (2015), 1550018  crossref  mathscinet  zmath  isi  elib  scopus
    43. Zhang L., Wahba G., Yuan M., “Distance shrinkage and Euclidean embedding via regularized kernel estimation”, J. R. Stat. Soc. Ser. B-Stat. Methodol., 78:4 (2016), 849–867  crossref  mathscinet  isi  elib  scopus
    44. Lee J.O., Schnelli K., Stetler B., Yau H.-T., “Bulk universality for deformed Wigner matrices”, Ann. Probab., 44:3 (2016), 2349–2425  crossref  mathscinet  zmath  isi  elib  scopus
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    46. Khorunzhiy O., “On High Moments of Strongly Diluted Large Wigner Random Matrices”, Seminaire de Probabilites Xlviii, Lect. Notes Math., Lecture Notes in Mathematics, 2168, eds. DonatiMartin C., Lejay A., Rouault A., Springer Int Publishing Ag, 2016, 347–399  crossref  mathscinet  isi  scopus
    47. Percy Deift, “Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II”, SIGMA, 13 (2017), 016, 23 pp.  mathnet  crossref
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    49. Lee J.O., Schnelli K., “Local Law and Tracy-Widom Limit For Sparse Random Matrices”, Probab. Theory Relat. Field, 171:1-2 (2018), 543–616  crossref  mathscinet  zmath  isi  scopus
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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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