论文标题
动态正弦模型的不变吉布斯动力学
Invariant Gibbs dynamics for the dynamical sine-Gordon model
论文作者
论文摘要
在本说明中，我们研究了具有参数$β^2> 0 $的双曲线随机阻尼正弦 - 戈登方程（SDSG），以及其在二维圆环上的相关Gibbs动力学。引入了合适的重新规定后，我们首先通过Barashkov-Gubinelli（2018）引起的变异方法构建了$ 0 <β^2 <4π$范围内的Gibbs测量。然后，我们证明，在$ 0 <β^2 <2π$范围内的双曲线SDSG动力学下，Gibbs测量的全局良好和不变性。我们的吉布斯度量的构建还可以确保吉布斯吉布斯量子级的正弦 - 戈登模型的吉布斯量度几乎确定，范围为$ 0 <β^2 <4π$。
In this note, we study the hyperbolic stochastic damped sine-Gordon equation (SdSG), with a parameter $β^2 > 0$, and its associated Gibbs dynamics on the two-dimensional torus. After introducing a suitable renormalization, we first construct the Gibbs measure in the range $0<β^2<4π$ via the variational approach due to Barashkov-Gubinelli (2018). We then prove almost sure global well-posedness and invariance of the Gibbs measure under the hyperbolic SdSG dynamics in the range $0<β^2<2π$. Our construction of the Gibbs measure also yields almost sure global well-posedness and invariance of the Gibbs measure for the parabolic sine-Gordon model in the range $0<β^2<4π$.
