Higher order concentration for functions of weakly dependent random variables
Higher order concentration for functions of weakly dependent random variables
复制标题
弱相关随机变量函数的高阶集中
DOI：
10.1214/19-ejp338
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发表时间：
2018
影响因子：
1.4
通讯作者：
A. Sinulis
中科院分区：
文献类型：
--
作者：
F. Gotze;H. Sambale;A. Sinulis
我们扩展最近的高阶浓度的结果在离散设置，包括可能的因变量的分布（在产品空间）满足对数Sobolev不等式相对于一个差分算子，从吉布斯采样器类型的动态功能。这样的随机变量的例子包括伊辛模型与n个节点一般，但弱相互作用，即在Dobrushin唯一性制度，我们证明浓度结果的齐次多项式，以及随机排列，切片的超立方体与动态给定的伯努利-拉普拉斯或对称简单的排斥过程。
We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a difference operator that arises from Gibbs sampler type dynamics. Examples of such random variables include the Ising model on a graph with n nodes with general, but weak interactions, i.e. in the Dobrushin uniqueness regime, for which we prove concentration results of homogeneous polynomials, as well as random permutations, and slices of the hypercube with dynamics given by either the Bernoulli-Laplace or the symmetric simple exclusion processes.
Ising模型多线性函数的集中及其在网络数据中的应用
DOI：
--
发表时间：
2017
期刊：
Annual Conference on Neural Information Processing Systems (NIPS
影响因子：
--
作者：
Daskalakis, Constantinos;Dikkala, Nishanth;Kamath, Gautam C.
通讯作者：
Kamath, Gautam C.