概率论中的不等式和Turán-Type彩色顶点图的问题

Random Struct. Algorithms Pub Date : 2007-07-05 DOI:10.1002/rsa.3240020107

A. Sidorenko

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引用次数: 3

摘要

对于独立且同分布的随机元素ζ和η，其P{(ζ， η)∧E}≧f(P{η∧D1}P{η∧Dm})型的“最佳”不等式可以简化为具有彩色顶点的图的图兰型问题。在目前的工作中，我们描述了一个有限算法来获得这类任意问题的渐近解。在两种颜色的情况下，我们无需使用该算法就得到了渐近解的最终形式。

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Inequalities in Probability Theory and Turán-Type Problems for Graphs with Colored Vertices

The “best” inequalities of type P{(ζ, η)⊂ E} ≧f(P{η⊂ D1}P{η⊂Dm}) for independent and identically distributed random elements ζ and η can be reduced to Turan-type problems for graphs with colored vertices. In the present work we describe a finite algorithm for obtaining the asymptotical solution for an arbitrary problem of such type. In the case of two colors we obtain the final form of asymptotic solution without using the algorithm.

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Random Struct. Algorithms

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