Central limit theorem for the Edwards model

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

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    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 languageEnglish
    Pages (from-to)573-597
    Number of pages25
    JournalThe Annals of Probability
    Volume25
    Issue number2
    Publication statusPublished - 1997

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