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).
Citation
W. König. F. den Hollander. R. van der Hofstad. "Central limit theorem for the Edwards model." Ann. Probab. 25 (2) 573 - 597, April 1997. https://doi.org/10.1214/aop/1024404412
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