论文标题
固定尺寸均匀绘制的子集的OSSS型不等式
An OSSS-type inequality for uniformly drawn subsets of fixed size
论文作者
论文摘要
OSS不平等[O'Donnell，Saks，Schramm and Servio，第46届年度IEEE IEE EEE研讨会上的计算机科学基础（FOCS'05），Pittsburgh（2005）]，为独立0-1的随机变量的随机变量和计算值的影响（即随机变量）的函数的变化提供了一个随机变量的差异，并具有一定的计算性变量，并具有一定的计算。 离开。 Duminil-Copin，Raoufi和Tassion [数学年鉴189，75-99（2019）]获得了对单调测量的概括，并将其用于证明Potts模型和随机群集模型的新结果。他们对OSS不平等的概括提出了一个问题，如果还有其他措施是否存在这种不平等的措施。我们为一个远离单调的度量家族而言，我们得出了OSS不等式的版本，即N量度的K-Out量度（这些度量与从一组n均匀的N尺寸N的绘制k元素相对应）。我们通过研究事件来说明不等式，即现场渗透模型中三角形晶格上的R Times R Box占据了水平穿越，其中盒子中确切的一半顶点被占据。
The OSSS inequality [O'Donnell, Saks, Schramm and Servedio, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05), Pittsburgh (2005)] gives an upper bound for the variance of a function f of independent 0-1 valued random variables, in terms of the influences of these random variables and the computational complexity of a (randomised) algorithm for determining the value of f. Duminil-Copin, Raoufi and Tassion [Annals of Mathematics 189, 75-99 (2019)] obtained a generalization to monotonic measures and used it to prove new results for Potts models and random-cluster models. Their generalization of the OSSS inequality raises the question if there are still other measures for which a version of that inequality holds. We derive a version of the OSSS inequality for a family of measures that are far from monotonic, namely the k-out-of-n measures (these measures correspond with drawing k elements from a set of size n uniformly). We illustrate the inequality by studying the event that there is an occupied horizontal crossing of an R times R box on the triangular lattice in the site percolation model where exactly half of the vertices in the box are occupied.
