This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like stochastic domination and coupling or Chernoff bounds for geometrically distributed random variables and for negatively correlated random variables. Most of the results presented here have appeared previously, some, however, only in recent conference publications. While the focus is on collecting tools for the analysis of randomized search heuristics, many of these may be useful as well in the analysis of classic randomized algorithms or discrete random structures.

中文翻译：

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用于分析随机优化启发式的概率工具

本章收集了几个被证明在随机搜索启发式分析中很有用的概率工具。这包括经典材料，如马尔可夫、切比雪夫和切尔诺夫不等式，但也包括一些鲜为人知的主题，如随机支配和耦合或几何分布随机变量和负相关随机变量的切尔诺夫边界。此处介绍的大多数结果以前都曾出现过，但也有一些仅出现在最近的会议出版物中。虽然重点是收集用于分析随机搜索启发式的工具，但其中许多工具在经典随机算法或离散随机结构的分析中也很有用。