随机群与性质（T）：再论杜德克定理
Random groups and Property (T): Żuk's theorem revisited
摘要：
我们提供了一个完整而严格的证明的一个定理归因于doouk，说明随机群在Gromov密度模型的d > 1/3具有性质（T）的概率很高。最初的论文有许多空白，特别是，没有描述涉及不同随机组模型之间传递的关键步骤。我们修复的差距，使用组合参数和最近的结果，关于完美匹配的随机超图。我们还提供了一个替代的证明，避免组合困难，仅依赖于G（n，p）模型中的随机图的谱性质。
英文摘要：
We provide a full and rigorous proof of a theorem attributed to Żuk, stating that random groups in the Gromov density model for d > 1/3 have property (T) with high probability. The original paper had numerous gaps, in particular, crucial steps involving passing between different models of random groups were not described. We fix the gaps using combinatorial arguments and a recent result concerning perfect matchings in random hypergraphs. We also provide an alternative proof, avoiding combinatorial difficulties and relying solely on spectral properties of random graphs in G(n, p) model.
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