We give a detailed asymptotic analysis of the profiles of random symmetric digital search trees, which are in close connection with the performance of the search complexity of random queries in such trees. While the expected profiles have been analyzed for several decades, the analysis of the variance turns out to be very difficult and challenging, and requires the combination of several different analytic techniques, including Mellin and Laplace transforms, analytic de‐Poissonization, and Laplace convolutions. Our results imply concentration of the profiles in the range where the mean tends to infinity. Moreover, we also obtain a two‐point concentration for the distributions of the height and the saturation level.

中文翻译：

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对称数字搜索树的节点概要文件：浓度属性

我们对随机对称数字搜索树的配置文件进行了详细的渐近分析，这与此类树中随机查询的搜索复杂度的性能密切相关。尽管已经对期望的轮廓进行了数十年的分析，但对方差的分析却非常困难且具有挑战性，并且需要将多种不同的分析技术（包括梅林变换和拉普拉斯变换，解析去泊松和拉普拉斯卷积）相结合。我们的结果表明轮廓集中在平均值趋于无穷大的范围内。此外，我们还获得了高度和饱和度分布的两点浓度。