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Multivariate Estimates for the Concentration Functions of Weighted Sums of Independent, Identically Distributed Random Variables
| Content Provider | Semantic Scholar |
|---|---|
| Author | Eliseeva, Yu. S. |
| Copyright Year | 2013 |
| Abstract | In this paper, we formulate and prove multidimensional generalizations of results obtained previously by the author and A. Yu. Zaitsev. Let X, X1, . . . , Xn be independent, identically distributed random variables. We study the behavior of the concentration function of the random variable ∑k=1nXkak$$ {\displaystyle \sum_{k=1}^n{X}_k{a}_k} $$ according to the arithmetic structure of the vectors ak. Recently, interest to this problem increased significantly due to study of distributions of eigenvalues of random matrices. In this paper, we formulate and prove some refinements of results of Rudelson–Vershinin and Friedland–Sodin. Bibliography: 29 titles. |
| Starting Page | 78 |
| Ending Page | 89 |
| Page Count | 12 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10958-014-2188-1 |
| Volume Number | 204 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1303.4005v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10958-014-2188-1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
