Central limit theorem for the Edwards model (Q1356357)

The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. The authors prove a central limit theorem for the endpoint of the path, extending a law of large numbers proved by \textit{J. Westwater} [in: Trends and developments in the eighties. Bielefeld Encounters Math. Phys. 4 and 5, 384-404 (1985; Zbl 0583.60066)]. The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of differential operators, introduced and analyzed by the first two authors [Commun. Math. Phys. 169, No. 2, 397-440 (1995; Zbl 0821.60078)]. It turns out to be independent of the strength of self-repellence and to be strictly smaller than one, which is the value for free Brownian motion.