RATES OF CONVERGENCE TO EQUILIBRIUM FOR POTLATCH AND SMOOTHING PROCESSES

• 成果类型: Article
• 署名作者: Banerjee, Sayan; Burdzy, Krzysztof
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1473
• 发表日期: 2021
• 页码: 1129-1163
• 关键词: dynamics; limit

摘要

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 Z(d).