连续介质中的Glauber动力学：一种构造性的态演化方法
Glauber Dynamics in Continuum: A Constructive Approach to Evolution of States
摘要：
对应于连续介质中相互作用粒子的无限系统的Glauber动力学，描述了态的演化。在微观和介观两个层次上进行描述。微观描述的基础上求解线性方程组的关联函数通过一个Ovsjannikov型的技术，产生的演化尺度的Banach空间。介观的描述是通过弗拉索夫尺度，这产生了一个线性的无限链的方程从那些关联函数。它的主要特点是，对于非齐次Poisson测度的初始关联函数，其解是这种测度的密度的关联函数，它解一个卷积型的非线性微分方程.
英文摘要：
The evolutions of states is described corresponding to the Glauber dynamics of an infinite system of interacting particles in continuum. The description is conducted on both micro- and mesoscopic levels. The microscopic description is based on solving linear equations for correlation functions by means of an Ovsjannikov-type technique, which yields the evolution in a scale of Banach spaces. The mesoscopic description is performed by means of the Vlasov scaling, which yields a linear infinite chain of equations obtained from those for the correlation function. Its main peculiarity is that, for the initial correlation function of the inhomogeneous Poisson measure, the solution is the correlation function of such a measure with density which solves a nonlinear differential equation of convolution type.
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