不等式证明中的概率方法

The Probabilistic Method in Inequality proving

在分析数学中有些不等式的证明往往比较复杂,而且具体的直观含义也比较抽象.如果能够建立起适当的概率模型,赋以一些随机事件或随机变量的具体含义,再利用概率论的理论加以证明,则常常能使证明过程得到简化.同时还可以为抽象的数学问题提供具体的概率背景,沟通各数学分支之间的联系.文中在分析数学的几个重要不等式的证明之中引进了概率方法,取得较好的效果.

In analysis mathematics, some identifications of inequalities are often more complicated, and concrete ocular meaning is more abstract. It can be applied to make the proving process simplified if some suitable probability models can be created and be given some concrete meanings of random events or random variables, and be proved by probability theory. Meanwhile, this can still provide a concrete probability background for abstract mathematics questions and build up some communicating between every mathematics branch. Better results are got during the course of the proofs of several inequalities in analysis mathematics by using probabilistic method.