论文标题
随机动态和应用于ISING模型的本地繁殖力不平等
The local Poincare inequality of stochastic dynamic and application to the Ising model
论文作者
论文摘要
受Parisi和Wu提出的随机量化的概念的启发，我们构建了通过随机微分方程在重生组中起着核心作用的过渡概率矩阵。通过建立离散的时间随机动力学，可以从概率的角度来表征重归其化过程。因此，我们将重点关注无限尺寸随机动态的研究。从随机的角度来看，离散的时间随机动态可以诱导马尔可夫链。通过计算方形磁场运算符和针对一类两点函数的Bakry-émery曲率，可以从从中获得相关函数的估计值。最后，在Ergodicity的条件下，通过选择系统参数$ k $与系统时间$ t $之间的夫妇关系在$ t \ rightarrow +\ infty $时正确，还估计了限制系统的两点相关功能。
Inspired by the idea of stochastic quantization proposed by Parisi and Wu, we construct the transition probability matrix which plays a central role in the renormalization group through a stochastic differential equation. By establishing the discrete time stochastic dynamics, the renormalization procedure can be characterized from the perspective of probability. Hence, we will focus on the investigation of the infinite dimensional stochastic dynamic. From the stochastic point of view, the discrete time stochastic dynamic can induce a Markov chain. Via calculating the square field operator and the Bakry-Émery curvature for a class of two-points functions, the local Poincaré inequality is established, from which the estimate of correlation functions can also be obtained. Finally, under the condition of ergodicity, by choosing the couple relationship between the system parameter $K$ and the system time $T$ properly when $T\rightarrow +\infty$, the two-points correlation functions for limit system are also estimated.
