论文标题
促进和平滑过程的收敛速率
Rates of convergence to equilibrium for Potlatch and Smoothing processes
论文作者
论文摘要
我们分析了平滑过程的局部和全球平滑速率，并在被称为Potlatch过程的双过程中获得了与平稳性的收敛速率。对于一般有限图，我们将平滑和收敛速率连接到关联的马尔可夫链的光谱间隙。我们对圆环上的这些过程进行了更详细的分析。获得对平滑速率的多项式校正。他们表明，本地平滑的发生速度比全球平滑速度快。这些多项式速率转化为$ \ 2 $ -Wasserstein距离的收敛速率，用于$ \ Mathbb {z}^d $。
We analyze the local and global smoothing rates of the smoothing process and obtain convergence rates to stationarity for the dual process known as the potlatch process. For general finite graphs, we connect the smoothing and convergence rates to the spectral gap of the associated Markov chain. We perform a more detailed analysis of these processes on the torus. Polynomial corrections to the smoothing rates are obtained. They show that local smoothing happens faster than global smoothing. These polynomial rates translate to rates of convergence to stationarity in $L^2$-Wasserstein distance for the potlatch process on $\mathbb{Z}^d$.
