条件泊松分布与色数的集中
Conditioned Poisson distributions and the concentration of chromatic numbers
摘要：
Achlioptis和Naor利用一个微妙的不等式建立了Erdos-Renyi随机图的色数的渐近集中性，本文给出了一个简单的证明方法.这些简化来自两个新的想法。第一个涉及一个尖锐的形式，一块统计民间传说的拟合优度测试双向表的泊松计数线性条件约束下。第二个想法采取的形式，一个新的不等式，控制极端的尾巴分布的二次型独立泊松随机变量。
英文摘要：
The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new ideas. The first involves a sharpened form of a piece of statistical folklore regarding goodness-of-fit tests for two-way tables of Poisson counts under linear conditioning constraints. The second idea takes the form of a new inequality that controls the extreme tails of the distribution of a quadratic form in independent Poissons random variables.
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