Geodesic
Limit theorems for random exponentials: the bounded support case
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 779-794

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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. 
@article{TVP_2018_63_4_a7,
     author = {M. Grabchak and S. A. Molchanov},
     title = {Limit theorems for random exponentials: the bounded support case},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {779--794},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a7/}
}
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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/