Convergence of path measures arising from a mean field or polaron type interaction
Convergence of path measures arising from a mean field or polaron type interaction
复制标题
由平均场或极化子型相互作用引起的路径测量的收敛
DOI：
10.1007/bf01192166
复制
发表时间：
1993
影响因子：
2
通讯作者：
Uwe Schmock
中科院分区：
文献类型：
--
作者：
E. Bolthausen;J. Deuschel;Uwe Schmock
讨论了具有平均场或极化子类型路径相互作用的马尔可夫过程的极限路径度量。在极化子类型的情况下，强度在时间轴上远距离衰减，因此相互作用在时间上是短范围的。相比之下，在平均场模型中，相互作用较弱，但在时间上具有较长的范围。Donsker和Varadhan证明了，对于配分函数，当通过使强度趋于零而增加范围时，当超过一个极限时，存在从极化子类型到平均场相互作用的转变。对路径措施的讨论则更为微妙。我们把平均场作为一个可微相互作用的例子，并讨论了从极化子类型到平均场相互作用的两个有指导意义的例子。
We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.