The law of an appropriately scaled sum of p -adic-valued, independent, identically and rotation-symmetrically distributed random variables weakly converges to a semi-stable law, if the tail probabilities of the variables satisfy some assumption. If we consider a scaled sum of such random variables with a sufficiently much higher scaling order, it accumulates to the origin, and the mass of any set not including the origin gets small. The purpose of this article is to investigate the asymptotic order of the logarithm of the mass of such sets off the origin. The order is explicitly given under some assumptions on the tail probabilities of the random variables and the scaling order of their sum. It is also proved that the large deviation principle follows with a rate function being constant except at the origin, and the rate function is good only for the case its value is infinity off the origin.

中文翻译：

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p-Adic 值旋转对称独立和同分布随机变量的缩放和的大偏差

如果变量的尾部概率满足某些假设，则适当缩放的 p 进值、独立、相同和旋转对称分布的随机变量的总和定律弱收敛到半稳定定律。如果我们考虑具有足够高缩放阶数的这些随机变量的缩放和，它会累积到原点，并且任何不包括原点的集合的质量都会变小。这篇文章的目的是研究这些衬托的质量的对数的渐近阶次。在对随机变量的尾部概率及其总和的缩放顺序的某些假设下，明确给出了顺序。还证明了大偏差原理遵循除了原点外的速率函数是恒定的，