Central limit theorem for the Edwards model. (English) Zbl 0873.60009

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 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.


60F05 Central limit and other weak theorems
60J55 Local time and additive functionals
60J65 Brownian motion
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