Anomalous behaviour for the random corrections to the cumulants of random walks in fluctuating random media

• 成果类型: Article
• 署名作者: Bernabei, MS
• 署名单位: University of Camerino
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/PL00008765
• 发表日期: 2001
• 页码: 410-432
• 关键词: CENTRAL-LIMIT-THEOREM; random environment; directed polymers

摘要

The Central Limit Theorem for a model of discrete-time random walks on the lattice Z(nu) in a fluctuating random environment was proved for almost-all realizations of the space-time environment, for all nu > 1 in [BMP1] and for all nu greater than or equal to 1 in [BBMP]. in [BMP1] it was proved that the random correction to the average of the random walk for nu greater than or equal to 3 is finite. In the present paper we consider the cases nu = 1, 2 and prove the Central Limit Theorem as T --> infinity for the random correction to the first two cumulants. The rescaling factor for the average is T-1/4 for nu = 1 and (ln T)(1/2), for nu = 2; for the covariance it is T1-nu /4, nu = 1,2.