On Optimal Bounds in the Local Semicircle Law under Four Moment Condition

Götze F, Naumov AA, Tikhomirov AN (2019)
DOKLADY MATHEMATICS 99(1): 40-43.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We consider symmetric random matrices , whose upper triangular entries are independent random variables with zero mean and unit variance. Under the assumption , j, k = 1, 2, ..., n, it is shown that the fluctuations of the Stieltjes transform m(n)(z), of the empirical spectral distribution function of the matrix about the Stieltjes transform of Wigner's semicircle law are of order (n). An application of the result obtained to the convergence rate in probability of the empirical spectral distribution function of to Wigner's semicircle law in the uniform metric is discussed.
Erscheinungsjahr
Zeitschriftentitel
DOKLADY MATHEMATICS
Band
99
Ausgabe
1
Seite(n)
40-43
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Götze F, Naumov AA, Tikhomirov AN. On Optimal Bounds in the Local Semicircle Law under Four Moment Condition. DOKLADY MATHEMATICS. 2019;99(1):40-43.
Götze, F., Naumov, A. A., & Tikhomirov, A. N. (2019). On Optimal Bounds in the Local Semicircle Law under Four Moment Condition. DOKLADY MATHEMATICS, 99(1), 40-43. doi:10.1134/S1064562419010125
Götze, F., Naumov, A. A., and Tikhomirov, A. N. (2019). On Optimal Bounds in the Local Semicircle Law under Four Moment Condition. DOKLADY MATHEMATICS 99, 40-43.
Götze, F., Naumov, A.A., & Tikhomirov, A.N., 2019. On Optimal Bounds in the Local Semicircle Law under Four Moment Condition. DOKLADY MATHEMATICS, 99(1), p 40-43.
F. Götze, A.A. Naumov, and A.N. Tikhomirov, “On Optimal Bounds in the Local Semicircle Law under Four Moment Condition”, DOKLADY MATHEMATICS, vol. 99, 2019, pp. 40-43.
Götze, F., Naumov, A.A., Tikhomirov, A.N.: On Optimal Bounds in the Local Semicircle Law under Four Moment Condition. DOKLADY MATHEMATICS. 99, 40-43 (2019).
Götze, Friedrich, Naumov, A. A., and Tikhomirov, A. N. “On Optimal Bounds in the Local Semicircle Law under Four Moment Condition”. DOKLADY MATHEMATICS 99.1 (2019): 40-43.