Optimal bounds for convergence of expected spectral distributions to the semi-circular law

Götze F, Tikhomirov A (2016)
PROBABILITY THEORY AND RELATED FIELDS 165(1-2): 163-233.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Let X = (X-jk)(j,k=1)(n) denote a Hermitian random matrix with entries X-jk, which are independent for 1 <= j <= k <= n. We consider the rate of convergence of the empirical spectral distribution function of the matrix X to the semi-circular law assuming that EX (jk) = 0, EXjk2 = 1 and that sup(n >= 1) sup(1 <= j, k <= n) E vertical bar X-jk vertical bar(4) =: mu(4) < infinity, and sup(1 <= j,k <= n) vertical bar X-jk vertical bar <= D(0)n(1/4) By means of a recursion argument it is shown that the Kolmogorov distance between the expected spectral distribution of the Wigner matrix W = 1/root nX and the semicircular law is of order O(n(-1)).
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Zeitschriftentitel
PROBABILITY THEORY AND RELATED FIELDS
Band
165
Ausgabe
1-2
Seite(n)
163-233
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Götze F, Tikhomirov A. Optimal bounds for convergence of expected spectral distributions to the semi-circular law. PROBABILITY THEORY AND RELATED FIELDS. 2016;165(1-2):163-233.
Götze, F., & Tikhomirov, A. (2016). Optimal bounds for convergence of expected spectral distributions to the semi-circular law. PROBABILITY THEORY AND RELATED FIELDS, 165(1-2), 163-233. doi:10.1007/s00440-015-0629-5
Götze, F., and Tikhomirov, A. (2016). Optimal bounds for convergence of expected spectral distributions to the semi-circular law. PROBABILITY THEORY AND RELATED FIELDS 165, 163-233.
Götze, F., & Tikhomirov, A., 2016. Optimal bounds for convergence of expected spectral distributions to the semi-circular law. PROBABILITY THEORY AND RELATED FIELDS, 165(1-2), p 163-233.
F. Götze and A. Tikhomirov, “Optimal bounds for convergence of expected spectral distributions to the semi-circular law”, PROBABILITY THEORY AND RELATED FIELDS, vol. 165, 2016, pp. 163-233.
Götze, F., Tikhomirov, A.: Optimal bounds for convergence of expected spectral distributions to the semi-circular law. PROBABILITY THEORY AND RELATED FIELDS. 165, 163-233 (2016).
Götze, Friedrich, and Tikhomirov, A. “Optimal bounds for convergence of expected spectral distributions to the semi-circular law”. PROBABILITY THEORY AND RELATED FIELDS 165.1-2 (2016): 163-233.