论文标题
修改后的日志贝贝尔不等式，贝克纳的不平等和力矩估计
Modified log-Sobolev inequalities, Beckner inequalities and moment estimates
论文作者
论文摘要
我们证明，在普通马尔可夫半群中，贝克纳的不平等现象从零分开，因为$ p \至1^+$等同于修改后的log sobolev不平等（以前只有一种含义在此通用性中存在）。此外，通过改编Boucheron等人的论点。我们得出了在这些功能不平等下存在的Sobolev类型矩估计。 我们用适用于各种随机模型的量度估计浓度（也是Lipschitz函数的情况）的应用，包括随机排列，零范围的过程，强瑞利测量值，指数随机图和Poisson路径路径空间上的几何函数。
We prove that in the context of general Markov semigroups Beckner inequalities with constants separated from zero as $p\to 1^+$ are equivalent to the modified log Sobolev inequality (previously only one implication was known to hold in this generality). Further, by adapting an argument by Boucheron et al. we derive Sobolev type moment estimates which hold under these functional inequalities. We illustrate our results with applications to concentration of measure estimates (also of higher order, beyond the case of Lipschitz functions) for various stochastic models, including random permutations, zero-range processes, strong Rayleigh measures, exponential random graphs, and geometric functionals on the Poisson path space.
