Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices
Götze F, Timushev DA, Tikhomirov AN (2021)
Doklady Mathematics 104(3): 332-335.
Zeitschriftenaufsatz
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Autor*in
Götze, FriedrichUniBi;
Timushev, D. A.;
Tikhomirov, A. N.
Einrichtung
Abstract / Bemerkung
We consider sparse sample covariance matrices with sparsity probability with p(n) >= c(0) log((aleph) over bar) n/n with aleph > 0. Assuming that the distribution of matrix elements has a finite absolute moment of order 4 + delta, delta > 0, it is shown that the distance between the Stieltjes transforms of the empirical spectral distribution function and the Marchenko-Pastur law is of order n(1/(nv) + 1/(np(n))), where v is the distance to the real axis in the complex plane.
Stichworte
local Marchenko-Pastur law;
local regime;
sparse random matrices;
spectrum of a random matrix;
Stieltjes transform
Erscheinungsjahr
2021
Zeitschriftentitel
Doklady Mathematics
Band
104
Ausgabe
3
Seite(n)
332-335
ISSN
1064-5624
eISSN
1531-8362
Page URI
https://pub.uni-bielefeld.de/record/2962433
Zitieren
Götze F, Timushev DA, Tikhomirov AN. Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices. Doklady Mathematics. 2021;104(3):332-335.
Götze, F., Timushev, D. A., & Tikhomirov, A. N. (2021). Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices. Doklady Mathematics, 104(3), 332-335. https://doi.org/10.1134/S1064562421060065
Götze, Friedrich, Timushev, D. A., and Tikhomirov, A. N. 2021. “Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices”. Doklady Mathematics 104 (3): 332-335.
Götze, F., Timushev, D. A., and Tikhomirov, A. N. (2021). Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices. Doklady Mathematics 104, 332-335.
Götze, F., Timushev, D.A., & Tikhomirov, A.N., 2021. Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices. Doklady Mathematics, 104(3), p 332-335.
F. Götze, D.A. Timushev, and A.N. Tikhomirov, “Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices”, Doklady Mathematics, vol. 104, 2021, pp. 332-335.
Götze, F., Timushev, D.A., Tikhomirov, A.N.: Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices. Doklady Mathematics. 104, 332-335 (2021).
Götze, Friedrich, Timushev, D. A., and Tikhomirov, A. N. “Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices”. Doklady Mathematics 104.3 (2021): 332-335.
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