Abstract:
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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