论文标题
关于二项式总和，加性能量和懒惰的随机步行
On binomial sums, additive energies, and lazy random walks
论文作者
论文摘要
我们建立了由de dios Pont，Greenfeld，Ivanisvili和Madrid在Arxiv的$ K $ addive-addive oddive oddive oddive oddive oddive oddive估计中，该估计值：2112.09352，该概念概述了凯恩和陶的结果。本说明证明了唯一缺少的成分，这是实数的基本不等式，以前仅以$ k \ leq100 $进行验证。我们还通过在整数晶格上进行懒惰的非对称简单随机步行来解释这种不平等。
We establish a sharp estimate for $k$-additive energies of subsets of the discrete hypercube conjectured by de Dios Pont, Greenfeld, Ivanisvili, and Madrid in arXiv:2112.09352, which generalizes a result by Kane and Tao. This note proves the only missing ingredient, which is an elementary inequality for real numbers, previously verified only for $k\leq100$. We also give an interpretation of this inequality in terms of a lazy non-symmetric simple random walk on the integer lattice.
