A few remarks on the operator norm of random Toeplitz matrices

Journal of Theoretical Probability

Volumn 23, Issue 1, 2010, Pages 85-108

  Adamczak, Radosław ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Random Toeplitz matrices

Indexed keywords

EID: 75749113743     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-008-0201-7     Document Type: Article

References (14)

1. Adamczak, R.: A tail inequality for suprema of unbounded empirical processes with applications to Markov chains. Electron. J. Probab. 13(34), 1000-1034 (2008).
2. Bai, Z. D.: Methodologies in spectral analysis of large-dimensional random matrices, a review. Stat. Sin. 9(3), 611-677 (1999).
3. Bose, A., Sen, A.: Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices. Electron. Commun. Probab. 12, 29-35 (2007).
4. Bryc, W., Dembo, A., Jiang, T.: Spectral measure of large Hankel, Markov and Toeplitz matrices. Ann. Probab. 34(1), 1-38 (2006).
5. de Acosta, A., Kuelbs, J., Ledoux, M.: An inequality for the law of the iterated logarithm. In: Probability in Banach spaces, IV, Oberwolfach, 1982. Lecture Notes in Math., vol. 990, pp. 1-29. Springer, Berlin (1983).
6. Einmahl, U., Li, D.: Characterization of LIL behavior in Banach space. Trans. Am. Math. Soc. 360, 6677-6693 (2008).
7. Fuk, D. H., Nagaev, S. V.: Probabilistic inequalities for sums of independent random variables. Teor. Veroyatnost. Primenen. 16, 660-675 (1971).
8. Giné, E., Latała, R., Zinn, J.: Exponential and moment inequalities for U-statistics. In: High Dimensional Probability II. Progr. Probab., vol. 47, pp. 13-38. Birkhäuser, Boston (2000).
9. Hammond, C., Miller, S. J.: Distribution of eigenvalues for the ensemble of real symmetric Toeplitz matrices. J. Theor. Probab. 18, 537-566 (2005).
10. Klein, T., Rio, E.: Concentration around the mean for maxima of empirical processes. Ann. Probab. 33, 1060-1077 (2005).
11. Ledoux, M., Talagrand, M.: Probability in Banach Spaces. Isoperimetry and Processes. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 23(3). Springer, Berlin (1991).
12. Meckes, M.: On the spectral norm of a random Toeplitz matrix. Electron. Commun. Probab. 12, 315-325 (2007).
13. Talagrand, M.: New concentration inequalities in product spaces. Invent. Math. 126(3), 505-563 (1996).
14. van der Vaart, A. W., Wellner, J. A.: Weak Convergence and Empirical Processes: With Applications to Statistics. Springer Series in Statistics. Springer, New York (1996).