Logarithmic Sobolev inequality for some models of random walks

• 成果类型: Article
• 署名作者: Lee, TY; Yau, HT
• 署名单位: University System of Maryland; University of Maryland College Park; New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 1855-1873
• 关键词: hydrodynamics

摘要

We determine the logarithmic Sobolev constant for the Bernoulli-Laplace model and the time to stationarity for the symmetric simple exclusion model up to the leading order. Our method for proving the logarithmic Sobolev inequality is based on a martingale approach and is applied to the random transposition model as well. The proof for the time to stationarity is based on a general observation relating the time to stationarity to the hydrodynamical limit.