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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 412, Pages 121–137
(Mi znsl5644)
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This article is cited in 6 scientific papers (total in 6 papers)
Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables
Yu. S. Eliseeva St. Petersburg State University, St. Petersburg, Russia
Abstract:
This article is a multidimensional generalization of the results Eliseeva and Zaitsev (2012). Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum_{k=1}^na_kX_k$ according to the arithmetic structure of vectors $a_k$. Recently the interest to this question has increased significantly due to the study of distributions of eigenvalues of random matrices. In this paper we formulate and prove some refinements of the results Friedland and Sodin (2007) and Rudelson and Vershynin (2009).
Key words and phrases:
multivarite concentration functions, sums of independent random variables, the Littlewood–Offord problem.
Received: 18.11.2012
Citation:
Yu. S. Eliseeva, “Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables”, Probability and statistics. Part 19, Zap. Nauchn. Sem. POMI, 412, POMI, St. Petersburg, 2013, 121–137; J. Math. Sci. (N. Y.), 204:1 (2015), 78–89
Linking options:
https://www.mathnet.ru/eng/znsl5644 https://www.mathnet.ru/eng/znsl/v412/p121
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Abstract page: | 234 | Full-text PDF : | 55 | References: | 48 |
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