Abstract
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).
Original language | English |
---|---|
Pages (from-to) | 573-597 |
Number of pages | 25 |
Journal | The Annals of Probability |
Volume | 25 |
Issue number | 2 |
Publication status | Published - 1997 |