Green-Tao-Ziegler稠密模型定理的新证明：一个说明
New Proofs of the Green-Tao-Ziegler Dense Model Theorem: An Exposition
摘要：
Green、Tao和Ziegler证明了以下形式的“稠密模型定理”：如果R是集合X的伪随机子集（可能非常稀疏），D是R的稠密子集，则D可以由一个集合M来建模，该集合M在X中的密度与D在R中的密度近似相同。更一般地说，他们表明，由伪随机测度优化的函数可以写为具有相同期望的有界函数加上与零“不可区分”的函数的和。这个定理在证明格林-陶定理中起着关键作用，格林-陶定理证明素数包含任意长的等差数列。本文给出了Green-Tao-Ziegler稠密模型定理的一个新的证明。我们指的是我们的完整文件的变体的结果与连接和应用计算复杂性理论，并以高尔斯'文件的应用证明技术的"分解，"结构，“和”transference'“定理在算术和极值组合（以及更广泛的调查等定理）。
英文摘要：
Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may be modeled by a set M whose density inside X is approximately the same as the density of D in R. More generally, they show that a function that is majorized by a pseudorandom measure can be written as a sum of a bounded function having the same expectation plus a function that is ``indistinguishable from zero.'' This theorem plays a key role in the proof of the Green-Tao Theorem that the primes contain arbitrarily long arithmetic progressions. In this note, we present a new proof of the Green-Tao-Ziegler Dense Model Theorem, which was discovered independently by ourselves and Gowers. We refer to our full paper for variants of the result with connections and applications to computational complexity theory, and to Gowers' paper for applications of the proof technique to ``decomposition, ``structure,'' and ``transference'' theorems in arithmetic and extremal combinatorics (as well as a broader survey of such theorems).
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