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


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).


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W. König. F. den Hollander. R. van der Hofstad. "Central limit theorem for the Edwards model." Ann. Probab. 25 (2) 573 - 597, April 1997.


Published: April 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0873.60009
MathSciNet: MR1434119
Digital Object Identifier: 10.1214/aop/1024404412

Primary: 60F05 , 60J55 , 60J65

Keywords: central limit theorem , Edwards model , Ray-Knight theorems

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 2 • April 1997
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