On equivalence of quenched and annealed statistical properties for conservative IID random dynamical systems

• 成果类型: Article; Early Access
• 署名作者: Dewitt, Jonathan; Dolgopyat, Dmitry
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University System of Maryland; University of Maryland College Park
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01531-8
• 发表日期: 2026-08-27
• 关键词: sure invariance-principle; LIMIT-THEOREMS; decay

摘要

In this paper, we prove several theorems relating annealed exponential mixing of the two-point motion with quenched properties of the one-point motion for conservative IID random dynamical systems. In particular, we show that annealed exponential mixing of the two-point motion implies quenched exponential mixing of the one-point motion. We also show that if the two-point motion satisfies annealed exponential mixing and the annealed central limit theorem with polynomial rate of convergence, then the one-point motion satisfies a quenched CLT. These results hold for all H & ouml;lder and Sobolev spaces of positive index. This establishes the quenched CLT in many new cases.