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van der Hofstad, R.; den Hollander, F.; König, W.

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

Ann. Probab. 25, No. 2, 573-597 (1997).
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.
Reviewer: M.Iosifescu (Bucureşti)

Cited in 4 Reviews
Cited in 13 Documents

MSC:

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

Keywords:

Edwards model; transformed path measure; law of large numbers; self-repellence

Citations:

Zbl 0583.60066; Zbl 0821.60078
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\textit{R. van der Hofstad} et al., Ann. Probab. 25, No. 2, 573--597 (1997; Zbl 0873.60009)
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References:

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