We investigate an asymptotic behaviour of probabilities of large deviations for normalized combinatorial sums. We find a zone in which these probabilities are equivalent to the tail of the standard normal law. Our conditions are similar to the classical Bernstein conditions. The range of the zone of the normal convergence can be of a power order.

中文翻译：

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关于组合和的大偏差

我们研究了归一化组合和的大偏差概率的渐近行为。我们找到了一个区域，其中这些概率相当于标准正态定律的尾部。我们的条件类似于经典的伯恩斯坦条件。正常会聚区的范围可以是幂级的。