Central limit theorem for the Edwards model

• 成果类型: Article
• 署名作者: van der Hofstad, R; den Hollander, F; König, W
• 署名单位: Utrecht University; Radboud University Nijmegen; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 573-597
• 关键词: polymer

摘要

The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. We prove a central limit theorem for the endpoint of the path, extending a law of large numbers proved by Westwater. The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of differential operators, introduced and analyzed by van der Hofstad and den Hollander. Interestingly, the scaled variance turns out to be independent of the strength of self-repellence and to be strictly smaller than one (the value for free Brownian motion).