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Multivariate asymptotic normality determined by high moments (2312.04246v1)
Published 7 Dec 2023 in math.PR and math.CO
Abstract: We extend a general result showing that the asymptotic behavior of high moments, factorial or standard, of random variables, determines the asymptotically normality, from the one dimensional to the multidimensional setting. This approach differs from the usual moment method which requires that the moments of each fixed order converge. We illustrate our results by considering a joint distribution of the numbers of bins (having the same, finite, capacity) containing a prescribed number of balls in a classical allocation scheme.
- E. A. Bender. Central and local limit theorems applied to asymptotic enumeration. J. Combin. Theory Ser. A 15 (1973), 91–111.
- Fringe trees for random trees with given vertex degrees. Preprint.
- P. Gao. Distribution of the number of spanning regular subgraphs in random graphs. Random Structures Algorithms 43 (2013), 338–353.
- A. N. Timashev. Limit theorems for allocations of particles over different cells with restrictions to the size of the cells. Theory Probab. Appl. 49 (2005), 659–670 (SIAM translation from Russian Journal).
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