Central limit theorem for the Edwards model

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 byWestwater (1984). The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of dierential operators, introduced and analyzed in van der Hofstad and den Hollander (1995). 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).