论文标题
关于弗雷德里克森·安德森（Fredrickson-Andersen）的注释
A note on the Fredrickson-Andersen one spin facilitated model in stationarity
论文作者
论文摘要
本说明讨论了与弗雷德里克森·安德森（Fredrickson-Andersen）相关的两个问题。 2008年在坎克里尼（Cancrini），马蒂内利（Martinelli），罗伯托（Roberto）和托尼尔利（Toninelli）的论文中考虑的第一个是该模型无限发电机的光谱差距。当密度较大时，他们研究了该频谱差距的衰减，但是在尺寸$ 3 $及更高的尺寸时，他们找不到确切的指数。他们还表明，该模型的持久性功能具有指数性的尾巴，但典型的衰减时间尚未分析。我们将看到，在尺寸$ 3 $ $ 3 $的频谱差距衰减的正确指数为$ 2 $，并发现持续函数衰减的时间如何衰减高密度。我们还讨论了有限图中光谱差距的缩放。
This note discusses two problems related to the Fredrickson-Andersen one spin facilitated model in stationarity. The first, considered in 2008 in a paper of Cancrini, Martinelli, Roberto and Toninelli, is the spectral gap of the model's infinitesimal generator. They study the decay of this spectral gap when the density is large, but in dimensions $3$ and higher, they do not find the exact exponent. They also show that the persistence function of the model has exponential tail, but the typical decay time is not analyzed. We will see that the correct exponent for the decay of the spectral gap in dimension $3$ and higher is $2$, and discover how the time over which the persistence function decays diverges in high densities. We also discuss the scaling of the spectral gap in finite graphs.
