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Limit theorems for random exponentials: the bounded support case
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 779-794 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study the asymptotic distributions, under appropriate normalization, of the sum $S_t = \sum_{i=1}^{N_t} e^{t X_i}$, the maximum $M_t = \max_{i\in\{1,2,\dots,N_t\}} e^{tX_i}$, and the $l_t$ norm $R_t=S_t^{1/t}$, when $N_t\to\infty$ as $t\to\infty$ and $X_1,X_2,\dots$ are independent and identically distributed random variables in the maximum domain of attraction of the reverse-Weibull distribution.
Keywords: random exponentials, exponential sums, random energy model. 
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M. Grabchak; S. A. Molchanov. Limit theorems for random exponentials: the bounded support case. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 779-794. http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a7/

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